
Luca LANZONI
Professore Associato Dipartimento di Ingegneria "Enzo Ferrari"

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2024
 Analytic insights on isotropic energy forms based on experiments of finite torsion
[Abstract in Atti di Convegno]
Falope, FEDERICO OYEDEJI; Lanzoni, Luca; Tarantino, Angelo Marcello
abstract
In finite torsion of cylinder a huge number of nonlinear complex effects occur: contraction of the radius, elongation of the cylinder, arising of axial force, and the onset of instability are fascinating effects induced by the fully nonlinear context. However, there is no trace in the literature of an exhaustive and complete work which fully investigates each case of torsion from a theoretical and experimental standpoint. Different cases of torsion are accounted for in the framework of nonlinear elasticity: free torsion and restrained torsion. For these cases of torsion, experiments are very rare in the literature for soft materials as they require extremely sophisticated devices for the measurement of displacement fields and forces. Moreover, the case of pure torsion, which leads to a fundamental universal relation of solid mechanics, was never investigated in terms of the reliability of its fundamental assumptions. We present a new set of experiments on the free torsion and restrained torsion of polyurethanes and silicon rubbers. Along with the torsion tests, uniaxial tests of the rubber are presented. Based on the experiments and universal relation of pure torsion, we experimentally proof the relevance of the second invariant of deformation. We point out that the relevance of the second deformation invariant decreases as the deformation increases. Characterization of the materials, by means of the best fit procedure of the experiments, shows how much the simultaneous fitting of multiple states of stress can reduce the quality of the fitting. Among the energy forms here considered, both incompressible and compressible, we show that only the compressible energy law can grasp the experimental Poynting elongation of the rubbers. In addition to the above, we propose a new formulation in nonlinear elasticity to predict the onset of instability in the case of restrained torsion.
2024
 Experimental investigation of catalan vault structures based on earthen
materials
[Articolo su rivista]
Franciosi, Mattia; Savino, Vincenzo; Lanzoni, Luca; Tarantino, Angelo Marcello; Viviani, Marco
abstract
The Catalan vaulting have succeeded in reducing reliance on support centers, resulting in lowered costs and expedited construction processes. This research advances the study of Catalan vaulting by exploring innovative, environmentally friendly earthbased materials. The study conducts a comprehensive comparative analysis of loadbearing behaviors across distinct vault elements: those fabricated from
terracotta, rawearth tiles, and shotearth. Constructed and tested at a 4meter span, fullscale vault specimens are subjected to varying distributed load configuration, followed by rupture testing employing a linear load at a quarter of the span. Experimental evidence, corroborated by FE results, indicates that both terracotta and raw earth tile vaults offer commendable performance, yet their failure
loads are surpassed by vaults constructed using shotearth. Therefore, shotearth emerges as a sustainable alternative for constructing vault elements. Furthermore, the study demonstrates that incorporating reinforcement within shotearth vaults increases their strength and ductility.
2024
 Large twisting of noncircular cylinders in unconstrained elasticity
[Articolo su rivista]
Falope, Federico; Lanzoni, Luca; Tarantino, Angelo Marcello
abstract
This paper deals with the equilibrium problem of noncircular cylinders subjected to finite torsion. A threedimensional kinematic model is formulated, where, in addition to the rigid rotation of the cross sections, the large twist of the cylinder also generates in and outofplane pure deformation of the cross sections and the variation of the cylinder length. Following the semiinverse approach, the displacement field prescribed by the above kinematic model contains an unknown constant, which governs the elongation of the cylinder, and three unknown functions which describe the pure deformation of the cross sections. A Lagrangian analysis is then performed and the compressible MooneyRivlin law is assumed for the stored energy function. Once evaluated the PiolaKirchhoff stresses, the boundary value problem is formulated. Nevertheless, the governing equations assume a coupled and nonlinear form which does not allow to apply standard solution methods. Therefore, the unknown functions are expanded into power series using polynomial terms in two variables. These series contain unknown constants which are evaluated applying the iterative Newton's method. With this procedure an accurate semianalytical solution has been obtained, which can be used to compute displacements,
stretches and stresses in each point of the cylinder. For the elliptical and rectangular sections, the results provided by the proposed solution method are shown by a series of graphs. Finally, the Poynting effect was investigated by varying the section shape of the cylinder.
2024
 Lateral buckling of a hyperleastic solid under finite bending
[Abstract in Atti di Convegno]
Falope, FEDERICO OYEDEJI; Lanzoni, Luca; Tarantino, Angelo Marcello
abstract
The problem of a beam that laterally buckles when subjected to flexure in the plane of greatest bending stiffness has been investigated first in the pioneering works by Prandtl and Michell in 1899. Those studies, and many others appeared in Literature afterwards, are based on the classical beam theory, which predicts that the cross sections experience a rigid rotation maintaining their original shape after deformation.
However, experimental investigations highlight that a more challenging scenario takes place when, instead of beamlike solids, platelike bodies are bent in their stiffest plane. In such a situation, an elastic deformation takes place also in the planes of the cross sections. This holds true particularly if large bending is needed to reach the onset of flexural–torsional buckling.
The present work addresses the problem of the lateral buckling of a hyperelastic prismatic body under finite bending accounting for the deformation of the cross sections also. The stored energy function for compressible MooneyRivlin materials is considered, thu accounting for both material and geometric nonlinearities. The problem is handled through the energy method. Starting from the bent configuration of the prism, an outofplane displacement field is superposed as a small perturbation. Then, the vanishing of the variation of the total potential energy allows assessing the critical angle (or, equivalently, the critical bending moment) for which a deflected equilibrium configuration adjacent to the purely bent one becomes possible. According to the energetic approach, the method provides upper bounds of the critical loads. However, it is shown that the accuracy of the solution may be conveniently improved by enriching the general expression of the perturbation.
2024
 Lateral buckling of the compressed edge of a beam under finite bending
[Articolo su rivista]
Falope, Federico; Lanzoni, Luca; Tarantino, Angelo Marcello
abstract
This paper investigates the critical condition whereby the compressed edge of a beam subjected to large bending exhibits a sudden lateral heeling. This instability phenomenon occurs through a mechanism different from that usually studied in linear theory and known as flexuraltorsional buckling. An experimental test device was specifically designed and built to perform pure bending tests on soft materials. Thus, the experimental campaign provides not only the momentcurvature behavior of beams of narrow rectangular cross section, but also information regarding the postcritical lateral buckling behavior. To study the local bifurcation phenomenon, an analytical model is proposed in which a field of small transversal displacements, typical of the linear stability of thin plates, is superimposed on the large vertical displacement field of an inflexed beam in the nonlinear elasticity theory. Furthermore, numerous numerical simulations through nonlinear FE analysis have been performed. Finally, the results provided by the different methods applied were compared and discussed.
2024
 ShotEarth as Sustainable Construction Material: Chemical Aspects and Physical Performance
[Articolo su rivista]
Barbieri, Luisa; Lanzoni, Luca; Marchetti, Roberta; Iotti, Simone; Tarantino, Angelo Marcello; Lancellotti, Isabella
abstract
Soil has long been one of the most widely used building materials globally. The evolution of soilbased construction materials has seen steady improvement over the centuries, even as traditional materials have given way to newer options like reinforced concrete. Nonetheless, soilbased construction has maintained its relevance and, in recent decades, has garnered increased attention due to sustainability concerns and renewed research interest. Among the innovative earthbased materials, shotearth (SE) stands out as one of the most advanced. Research on SE has facilitated efficient handling of soil variability in mix design and provided structural engineers with relevant models for dimensioning and detailing reinforced SE constructions. This paper focuses on studying the durability characteristics of various types of SE to ascertain their ability to withstand environmental degradation over their intended lifespan. The tests conducted indicate that SE can serve as a viable construction material in numerous reallife scenarios, offering a sustainable alternative to existing materials.
2024
 Structural design of reinforced earthcrete (ReC) beams
[Articolo su rivista]
Franciosi, M.; Savino, V.; Lanzoni, L.; Tarantino, A. M.; Viviani, Marco
abstract
This paper presents the results of an extensive experimental campaign aimed at evaluating the feasibility of using steelreinforced earthen materials for loadbearing structural applications, with a focus on a new category termed "shotearth". Addressing excavated soil, a major source of construction waste, shotearth demonstrates remarkable properties, such as notable green strength and reduced water sensitivity. The experimental program includes fourpoint bending tests on steelreinforced shotearth beams, along with pullout tests to assess the adherence between ribbed steel bars and shotearth. A flexural design approach, traditionally suited for reinforced concrete,
is presented and validated to establish a reliable model for reinforced shotearth elements in bending state. These findings suggest that leveraging existing models for reinforced concrete can overcome some traditional challenges associated with earthbased constructions, promoting them as a viable and ecological alternative to conventional construction materials.
2023
 Changing the approach to sustainable constructions: An adaptive mixdesign calibration process for earth composite materials
[Articolo su rivista]
Franciosi, M.; Savino, V.; Lanzoni, L.; Tarantino, A. M.; Viviani, M.
abstract
One major drawback of excavation earthbased composite construction materials is the variability in excavation earth characteristics from site to site. This variability can affect certain physical properties, and, in turn, the design models used to create a structure. To solve this problem, a methodology has been developed to predict the physical properties of earthbased composites for any mixdesign variation, which enables a robust structural design process. This new methodology has been tested for Shotearth, a new class of earthbased composite material made using high rates of excavation earth, aggregates, and a low rate of stabilization if needed. Shotearth is placed using a highspeed drymix process. The methodology was tested by preparing small, inexpensive specimens through a process that simulates the
dryprocess used to fabricate Shotearth in the field. An adaptive technique, used in conjunction with the experimental methodology, allows for the identification of the variant of possible Shotearth mixdesigns that provides optimal physical properties for a specific project. This technique is potentially applicable to any type of earthbased composite. The proposed methodology’s reliability enables a fast and costeffective detailing of Shotearth constructions.
2023
 Elastic solution for a circular disk with a central crack under compressive diametrical load
[Abstract in Atti di Convegno]
Radi, E.; Lanzoni, L.
abstract
The splitting tensile strength test (Brazilian test) is widely used because of its simplicity to assess the ultimate tensile strength and fracture behaviour of a variety of brittle materials, with specific reference to ceramics, concrete, and cementitious composites. Indeed, from the linear theory of elasticity, the distribution of the normal stress along any diameter of an uncracked disk subjected to a pair of concentrated diametrical compressive forces is known in closed form. Conversely, a Brazilian disk with a preexisting central crack of a given length turns out to be a much more challenging problem owing to the mixed boundary conditions to be imposed inside and outside the crack along the crack direction, together with the condition about the stress field along the outer curved boundary of the disk.
Few studies deal with such a demanding layout. Among these, based on the weight function method, Dong et al. (2004) evaluated the SIFs varying the angle of the external load with respect the crack plane and the crack length as well. Critical conditions for the achievement of pure mode I and mode II loading have been found also. However, that study is restricted to the neighbouring of the crack tips.
In the present study, the full field solution of the Brazilian disk is provided analytically in terms of Airy stress function in bipolar coordinates. The study is handled by examining separately a skewsymmetric and a symmetric loading condition, representative for the mode II and mode I loadings, respectively. Both the situations lead to a Fredholm hypersingular integral equation, whose solution is found through a collocation method by expanding the unknown in series of Chebyshev polynomials. It is pointed out that for mode I loading, a closing or an opening crack may arise. Both these circumstances have been analysed in detail. Conversely to the existing studies, the proposed formulation allows assessing both the displacement and stress fields along the entire diameter of the disk in the direction of the crack for any loading angle.
2023
 Large Deformations and Stability of the TwoBar Truss Under Vertical Loads
[Capitolo/Saggio]
Pelliciari, M.; Falope, F. O.; Lanzoni, L.; Tarantino, A. M.
abstract
Analytical formulations for the static equilibrium of truss structures are often based on concepts of linear elasticity. Geometric nonlinearities are taken into account, but the nonlinear constitutive behavior of the material is not considered. However, the assumption of linear elastic material is not consistent with the response of solids subjected to large deformations. In light of this, accurate models must take into account both geometric and constitutive nonlinearities. In the present work, we investigate the problem of the von Mises (or twobar) truss subjected to a vertical load. The bars of the truss are composed of rubber so as to observe large displacements and deformations. We propose a theoretical model that is entirely developed in threedimensional nonlinear elasticity. A compressible MooneyRivlin law is employed for the constitutive behavior of the rubber. Experimental tests on the von Mises truss subjected to a vertical load are carried out. Snapthrough is observed and good agreement is found with the analytical predictions. Finally, a simple formulation to predict the critical Euler buckling load is presented and validated through experimental observation.
2023
 ShotEarth: A Material for Structural Engineering
[Capitolo/Saggio]
Savino, V.; Franciosi, M.; Lanzoni, L.; Tarantino, A. M.; Viviani, M.
abstract
2023
 The Challenge of Designing a New Class of EarthBased Composites Able to Increase the Circularity and Sustainability of the Construction Market
[Capitolo/Saggio]
Savino, V.; Franciosi, M.; Lanzoni, L.; Tarantino, A. M.; Viviani, M.
abstract
2023
 Theoretical and experimental analysis of the von Mises truss subjected to a horizontal load using a new hyperelastic model with hardening
[Articolo su rivista]
Pelliciari, Matteo; Falope, FEDERICO OYEDEJI; Lanzoni, Luca; Tarantino, Angelo Marcello
abstract
The von Mises truss has been widely studied in the literature because of its numerous applications in multistable and morphing structures. The static equilibrium of this structure was typically addresses by considering only geometric nonlinearities. However, Falope et al. (2021) presented an entirely nonlinear solution in finite elasticity and demonstrated that material nonlinearities play an important role in the prediction of both snapthrough and Euler buckling. In such work, the von Mises truss was subjected to a vertical load and thus the system was symmetric and the deformations were relatively small. The present contribution extends the investigation to the case of a horizontal load, which is much more complex due to asymmetry and very large deformations. Since most rubbers employed in technological applications exhibit hardening under large stretches, we propose a new hyperelastic model capable of reproducing this behavior. The advantage of such model compared to the ones available in the literature is that the equilibrium solution maintains a straightforward mathematical form, even when considering compressibility of the material. In addition, in this work we present a new formulation in nonlinear elasticity to predict Euler buckling. The formulation takes into account shear deformation. The analytical prediction agrees well with both finite element (FE) and experimental results, thus demonstrating the accuracy of the proposed model.
2022
 2D Green’s functions for an elastic layer on a rigid support loaded by an internal point force
[Articolo su rivista]
Falope, Federico; Lanzoni, Luca; Radi, Enrico
abstract
The problem of a homogeneous isotropic elastic layer resting on a rigid base and loaded by an internal point force is analytically investigated under plane strain conditions. The displacement field is sought as the superposition of a fundamental solution (doublet state) and a homogeneous solution which allows satisfying the boundary conditions at the upper and lower boundaries of the layer. The displacement field is represented through convergent Fourier integral transforms.
Once the closed form solution in the transformed domain is found, the displacement and stress fields are assessed by numerical inversion of transforms. Results concerning both the displacements and stresses for different positions of the load application point are reported and
compared to FEM solution, finding very good agreement. The solutions obtained for horizontal and vertical point forces define the Green’s functions for the layer, which can be used to describe the mechanical interaction between the layer and an embedded body. As a striking application,
the interaction between an elastic layer and an embedded laterally loaded wall or diaphragm is finally addressed, finding the contact pressure and, in turn, the internal forces in the diaphragm.
2022
 A cohesivebased FE interface for concrete members retrofitted with ultra performance cementitious mortars
[Abstract in Atti di Convegno]
Savino, V; Lanzoni, L.; Tarantino, Am; Viviani, M
abstract
2022
 A continuum model for graphene in nonlinear elasticity and its green applications
[Abstract in Atti di Convegno]
Pelliciari, Matteo; Tarantino, Angelo Marcello; Lanzoni, Luca
abstract
2022
 An AutoCalibrating SemiAdiabatic Calorimetric Methodology for Strength Prediction and Quality Control of Ordinary and UltraHighPerformance Concretes
[Articolo su rivista]
Viviani, Marco; Lanzoni, Luca; Savino, Vincenzo; Tarantino, Angelo Marcello
abstract
A timely knowledge of concrete and ultrahighperformance concrete (UHPC) strength is possible through the socalled strengthequivalent time (Et) curves. A timely knowledge of concrete strength is useful, for instance, to precisely determine when the shores of a hardening structural element can be safely removed. At the present time, the preparation of the strengthEt curves requires timeconsuming and laborintensive testing prior to the beginning of construction operations. This paper proposes an innovative method to derive the strengthEt and total heatEt curves for both normal strength and UHPC. Results confirmed that the proposed method is fast, inexpensive, selfcalibrating, accurate and can detect any variation of the concrete mix proportions or components quality. In addition, the quality of predictions of strength–maturity curves can be constantly improved as the specimens’ population increases. Finally, results obtained with the proposed method were compared with those obtained using standard methods, showing a good agreement.
2022
 Analytical and experimental study of snapthrough instability in truss
structures
[Abstract in Atti di Convegno]
Pelliciari, Matteo; Falope, FEDERICO OYEDEJI; Lanzoni, Luca; Tarantino, Angelo Marcello
abstract
Abstract
2022
 Experimental characterization and predictive modeling of the flexural behavior of HPFRC/UHPFRC beams
[Abstract in Atti di Convegno]
Savino, V.; Lanzoni, L.; Tarantino, A. M.; Viviani, M.
abstract
The high manufacturing costs of UHPFRC applications together with timeconsuming tests re
quested for the characterization and control quality restrict a wider application of this kind of smart
material in the field of the rehabilitation of concrete structures. For this purpose, predictive strength
models are useful to reduce this kind of and, at the same time, optimize the amount of compounds
in the mixture according to the design requirements, for example by detecting the minimal dosage of
fibers necessary to attain the design tensile strength. At the present, no predictive strength models
suitable for HPFRC/UHPFRC are available. This work proposes a model able to predict the mechanical
response of HPFRC/UHPFRC for any change of matrix and fiber properties. The reliability of the
proposed model was confirmed from a large experimental investigation performed on smart concrete
mixes.
2022
 Finite Torsion of Compressible Circular Cylinders: An Approximate Solution
[Articolo su rivista]
Falope, F. O.; Lanzoni, L.; Tarantino, A. M.
abstract
This paper deals with the equilibrium problem of circular cylinders under finite torsion. A threedimensional kinematic model, where the large twisting of the cylinder is accompanied by transverse contraction and longitudinal extension, is formulated. Following a semiinverse approach, the displacement field prescribed by the above kinematic model contains as unknowns the longitudinal displacement, the rigid rotation and the transverse stretch of cross sections. To simplify the mathematical formulation, the transverse stretch is assumed to be constant, as it radially undergoes very low variations. This hypothesis produces some approximations in the field equations, but the equilibrium solution obtained is however characterized by a satisfactory accuracy, as shown by the comparisons performed using the numerical techniques of the Finite Element Method (FEM). A Lagrangian analysis is performed and the compressible MooneyRivlin law is assumed for the stored energy function. Once evaluated the PiolaKirchhoff stresses, the unknowns are determined by imposing the equilibrium conditions and the boundary conditions. For the end base of the cylinder two
different boundary conditions have been considered, according to which the longitudinal translation of this surface is allowed or prevented. Once the kinematic unknowns have been determined, explicit formulae for displacements, stretches and stresses are provided, which show the role of the geometric and constitutive parameters, as well as of the twisting angle. The results provided by the proposed solution are shown by a series of graphs. The same torsion problem has been addressed with FEM. A very good agreement was found between the results obtained with the two different analyses. Finally, the nonlinear torsion problem was linearized by introducing the hypothesis of smallness of the displacement and deformation fields. With this linearization, the classical solution for the infinitesimal torsion problem was fully retrieved.
2022
 Finite bending of nonslender beams and the limitations of the Elastica theory
[Articolo su rivista]
Falope, FEDERICO OYEDEJI; Lanzoni, Luca; Tarantino, Angelo Marcello
abstract
The problem of slender solids under finite bending has been addressed recently in Lanzoni and Tarantino (2018). In the present work, such a model is extended to short solids by improving the background formulation. In particular, the model is refined by imposing the vanishing of the axial force over the cross sections. The geometrical neutral loci, corresponding to unstretched and unstressed surfaces, are provided in a closed form. Two approximations of the models are obtained linearising both kinematics and constitutive law and kinematics only. It is shown that the approximations of the model, corresponding to the Euler Elastica formulation, can lead to significant values of the axial stress resultants despite pure bending conditions. For a generic form of compressible energy function, a nonlinear moment–curvature relation accounting for both material and geometric nonlinearities is provided and then specialised for a Mooney–Rivlin material. The obtained results are compared with simulations of 3D finite element models providing negligible errors. The normalisation of the moment–curvature relation provides the dimensionless bending moment as a function of the Eulerian slenderness of the solid. This dimensionless relation is shown to be valid for any aspect ratio of the bent solid and, in turn, it highlights the limitations of the Elastica arising in case of large deformations of solids.
2022
 Finite torsion of compressible hyperelastic cylinders: from simple to restrained torsion
[Abstract in Atti di Convegno]
Falope, Federico; Lanzoni, Luca; Tarantino, Angelo Marcello
abstract
Abstract
2022
 Green functions for an elastic layer on a rigid base and related problems
[Abstract in Atti di Convegno]
Falope, FEDERICO OYEDEJI; Lanzoni, Luca; Radi, Enrico
abstract
Abstract
2022
 Multiphase homogenization procedure for estimating the mechanical properties of shotearth materials
[Articolo su rivista]
Bacciocchi, M.; Savino, V.; Lanzoni, L.; Tarantino, A. M.; Viviani, M.
abstract
The paper proposes an analytical homogenization procedure to predict the overall elastic properties of shotearth, a sustainable composite material made of excavated soil, aggregates and, if needed, a binder for stabilization. A multistep methodology based on the Mori–Tanaka approach is used to account for the stabilized soil inclusions. This approach is proposed in order to shorten the mixdesign procedures and readily provide to the structural engineers a set of mechanical properties of the shotearth components to be used in the early design phases, when the construction field is not open yet and excavation of the site has not begun. The analytical results were successfully validated through an experimental campaign.
2022
 Predictive models for the ultimate tensile and compressive strengths of HPFRC/UHPFRC
[Abstract in Atti di Convegno]
Savino, V.; Lanzoni, L.; Tarantino, A. M.; Viviani, M.
abstract
Smart fiber reinforced cementitious composites, like HPFRC and UHPFRC, are today widely ap
plied in the field of the rehabilitation of concrete structures. However, one of the main drawback of
HPFRC/UHPFRC is that any modification of the matrixfibers mix design, due to the market require
ments, affects the mechanical properties of the hardened smart concrete, thus making useless tests
performed on previous version of the smart material. For this purpose prediction strength models that
link the properties of both fibers and matrix to the performances of the smart concrete are of great
practical interest. This work presents a simple and effective model that predicts the compressive and
tensile strengths of HPFRC as the fiber properties change. The predictive data obtained by the proposed
model were compared to experimental data, showing a good agreement.
2022
 Resistivity contribution tensor for nonconductive sphere doublets
[Articolo su rivista]
Lanzoni, L; Radi, E.
abstract
The distribution of the temperature and heat flux fields around a couple of unequal nonconductive tangent spherical inhomogeneities (or pores) embedded in an infinite medium under a steadystate and remotely applied heat flux is addressed in the present work. Owing to the 3D geometrical layout of the inhomogeneity, use is made of the tangent sphere coordinate system. A corrective temperature field expressed in terms of convergent integrals is superposed to the fundamental one to fulfill the BCs at the surfaces of the spheres. When the heat flux is aligned to the symmetry axis (axisymmetric problem), the solution can be found straightforwardly by introducing a stream function, which allows for transforming the Neumann BCs into a Dirichlet boundary value problem. Conversely, for the transversal heat flux (nonaxisymmetric problem), the problem is formulated in terms of temperature, thus leading to a system of two ODEs which is handled numerically through a Euler shooting method, after preliminary asymptotic expansions.
Once the temperature fields are known, the components of the resistivity contribution tensor are assessed varying the aspect ratio of the two spheres. It is found that the extrema of the thermal resistivity are achieved for spheres of equal size. The study allows assessing the effective thermal conductivity of a wide range of smart composites involving insulating inhomogeneities resembling sphere doublets.
2022
 Resistivity contribution tensor for two nonconductive overlapping spheres having different radii
[Articolo su rivista]
Lanzoni, Luca; Radi, Enrico; Sevostianov, Igor
abstract
We consider here the problem of a threedimensional (3D) body subjected to an arbitrarily oriented and remotely applied stationary heat flux. The body includes a nonconductive inhomogeneity (or pore) having the shape of two intersecting spheres with different radii. Using toroidal coordinates, the steadystate temperature field and the heat flux have been expressed in terms of Mehler–Fock transforms. Then, by imposing Neumann BCs at the surface of the spheres, a system of two Fredholm integral equations is obtained and solved based on Gauss–Laguerre quadrature rule. It is shown
that the components of the resistivity contribution tensor exhibit a nonmonotonic trend with the distance between sphere centers. In particular, if the inhomogeneity has a symmetric dumbbellshape, then the extrema of the resistivity contribution tensor components occur when the two overlapping spheres have the same size. Differently, when the inhomogeneity has a lenticular shape, then these extrema are attained for a nonsymmetric configuration, namely, for different radii of the intersecting spheres.
2022
 The formation and growth of a cross kink in a rope under torsion: An interpretation based on structural mechanics
[Articolo su rivista]
Lanzoni, L.; Tarantino, A. M.
abstract
The application of large twistings to a thin rope is known to cause the occurrence and evolution of an intermediate cross kink. Using classical linear elastic structural mechanics, the branched equilibrium path, which characterizes the kink formation, has been obtained. This path is characterized by increasing torsional stiffness. Some energy considerations have been formulated to motivate why the rope moves along the branched path generating the cross kink.
2021
 A FE model simulating the damage pattern along the interface of retrofitted cementbased members
[Relazione in Atti di Convegno]
Savino, V.; Lanzoni, L.; Tarantino, A. M.; Viviani, M.
abstract
2021
 Bending of nanobeams in finite elasticity
[Articolo su rivista]
Lanzoni, Luca; Tarantino, Angelo Marcello
abstract
Motivated by the need to have a fully nonlinear beam model usable at the nanoscale, in this paper, the equilibrium problem of inflexed nanobeams in the context of nonlocal finite elasticity is investigated. Considering both deformations and displacements large, a threedimensional kinematic model has been proposed. Extending the linear nonlocal Eringen theory, a constitutive law in integral form for the nonlocal Cauchy stress tensor has been defined. Finally, by imposing the equilibrium conditions, the governing equations are obtained. These take the form of a coupled system of three equations in integral form, which is solved numerically. Explicit formulae for displacements, stretches and stresses in every point of the nanobeam are derived. By way of example, a simply supported nanobeam, which is inflexed under nonlinear conditions, has been considered. The nonlocal effects on the deformation and internal actions are shown through some graphs and discussed in detail.
2021
 Dispositivo per l'isolamento di apparecchiature industriali, strutture e infrastrutture civili basato su moduli reticolari a traliccio
[Brevetto]
Falope, FEDERICO OYEDEJI; Lanzoni, Luca; Pelliciari, Matteo; Tarantino, Angelo Marcello; Salardi, Enrico
abstract
2021
 Effect of pore coalescence on the effective conductivity of an isotropic material
[Relazione in Atti di Convegno]
Radi, E.; Lanzoni, L.; Sevostianov, I.
abstract
The purpose of this work is to evaluate effect of two coalesced pores or insulating inhomogeneities on the overall conductive properties of an isotropic material. Analytical modeling of the effective properties of materials with microstructures formed by inhomogeneities of nonellipsoidal shape has not been well developed. The inhomogeneities are typically assumed to be ellipsoids of identical aspect ratios. This unrealistic assumption is largely responsible for insufficient linkage between methods of micromechanics and material science applications. The resistivity contribution tensor gives the extra temperature gradient produced by introduction of the inhomogeneity into a material subjected to otherwise uniform heat flux. The main goal of this work is to obtain an analytical solution for the components of the resistivity contribution tensor of two overlapping pores, in the 2D and 3D frameworks [1, 2].
2021
 Large nonuniform bending of beams with compressible stored energy functions of polynomialtype
[Articolo su rivista]
Lanzoni, Luca; Tarantino, Angelo Marcello
abstract
The large bending of beams made with complex materials finds application in many emerging fields. To describe the nonlinear behavior of these complex materials such as rubbers, polymers and biological tissues, stored energy functions of polynomialtype are commonly used. Using polyconvex and compressible stored energy functions of polynomialtype, in the present paper the equilibrium problem of slender beams in the fully nonlinear context of finite elasticity is formulated. In the analysis, the bending is considered nonuniform, the complete threedimensional kinematics of the beam is taken into account and both deformation and displacement fields are deemed large. The governing equations take the form of a coupled system of three equations in integral form, which is solved numerically through an iterative procedure. Explicit formulae for displacements, stretches and stresses in every point of the beam, following both Lagrangian and Eulerian descriptions, are derived. By way of example, a complete analysis has been performed for the Euler beam.
2021
 Nonuniform bending theory of hyperelastic beams in finite elasticity
[Articolo su rivista]
Lanzoni, L.; Tarantino, M.
abstract
This paper deals with the equilibrium problem of slender beams inflexed under variable curvature in the framework of fully nonlinear elasticity. For the specific case of uniform flexion, the authors have recently proposed a mathematical model. In that analysis, the complete threedimensional kinematics of the beam is taken into account and both deformations and displacements are considered large. In the present paper, the kinematics of the aforementioned model has been reformulated taking into account beams under variable curvature. Subsequently, focusing on the local determination of the curvature, new equilibrium conditions on cross sections are introduced in the mathematical formulation. The governing equations take the form of a coupled system of three equations in integral form, which is solved numerically through an iterative procedure. Therefore, for the generic class of hyperelastic and isotropic materials, explicit formulae for the displacement field, the stretches and stresses in every point of the beam, following both Lagrangian and Eulerian descriptions, are derived. The analysis allows studying a very wide class of equilibrium problems for nonlinear beams under different restraint conditions and subject to generic external load systems. By way of example, the Euler beam has been considered and the formulae obtained have been specialized for a specific neoprene rubber material, the constitutive constants of which have been determined experimentally. The shapes assumed by the beam as the load multiplier increases are shown through some graphs. The distributions of stretches and Cauchy stresses are plotted for the most stressed cross section. Some comparisons are made using a FE code. In addition, the accuracy of the obtained solution is estimated by evaluating a posteriori that the equilibrium equations are locally satisfied.
2021
 On the anticlastic bending of solids at finite strains
[Abstract in Atti di Convegno]
Falope, Fo; Lanzoni, L; Tarantino, Am
abstract
The present work deals with the problem of compressible isotropic hyperelastic solids under finite bending. The problem is fully nonlinear and, conversely to the classical Rivlin solution [1], it is formulated in the framework of threedimensional kinematics involving both large displacements and strains according to the context of finite elasticity. The model entails three kinematic assumptions, which stand for the planarity of the cross sections (BernoulliNavier hypothesis), the invariance of the curvature along the longitudinal direction of the solid (uniform bending) and the curvature of the cross sections (anticlastic curvature), that is assumed constant along the width of the solid [2]. Based on the semiinverse approach and according to the kinematic assumptions, the 3D displacement field is found, and, in turn, the deformation gradient is assessed. Then, the equilibrium conditions, specialized for a compressible MooneyRivlin material, provide proper relations among the unknown kinematic parameters, thus leading to the closure of the problem. Emphasis in placed on the “momentcurvature relation”, which is found to be governed by two independent dimensionless parameters: the Eulerian slenderness and the compactness index of the solid cross sections [3]. Similarity is observed with respect the previous works of Lamb (1890) regarding the mechanical response of bent plates and the experiments performed by Searle (1933) as well. Moreover, such an analysis allows broadening the “Elastica” to the more general context of finite elasticity.
In this work, the main results provided by the theoretical model are compared with those obtained by FE simulations and an experimental investigation based on a specifically designed mechanical apparatus, founding good agreement also for the case of extremely inflexed solids.
2021
 Silicon crystals for steering highintensity particle beams at ultrahighenergy accelerators
[Articolo su rivista]
Mazzolari, A.; Romagnoni, M.; Bagli, E.; Bandiera, L.; Baricordi, S.; Camattari, R.; Casotti, D.; Tamisari, M.; Sytov, A.; Guidi, V.; Cavoto, G.; Carturan, S. M.; De Salvador, D.; Balbo, A.; Cruciani, G.; Nhi Tran Caliste, Thu; Verbeni, R.; Pastrone, N.; Lanzoni, L.; Rossall, A.; van den Berg, J. A.; Jenkins, R.; Dumas, and P.
abstract
Experimental results and simulation models show that crystals might play a relevant role for the development of new generations of highenergy and highintensity particle accelerators and might disclose innovative possibilities at existing ones. In this paper we describe the most advanced manufacturing techniques of crystals suitable for operations at ultrahigh energy and ultrahigh intensity particle accelerators, reporting as an example of potential application the collimation of the particle beams circulating in the Large Hadron Collider at CERN, which will be upgraded through the addition of bent crystals in the frame of the High Luminosity Large Hadron Collider project.
2021
 Snapthrough and Eulerian buckling of the bistable von Mises truss in nonlinear elasticity: A theoretical, numerical and experimental investigation
[Articolo su rivista]
Falope, F. O.; Pelliciari, M.; Lanzoni, L.; Tarantino, A. M.
abstract
In this paper, the equilibrium and stability of the von Mises truss subjected to a vertical load is analyzed from theoretical, numerical and experimental points of view. The bars of the truss are composed of a rubber material, so that large deformations can be observed. The analytical model of the truss is developed in the fully nonlinear context of finite elasticity and the constitutive behavior of the rubber is modeled using a Mooney–Rivlin law. The constitutive parameters are identified by means of a genetic algorithm that fits experimental data from uniaxial tests on rubber specimens. The numerical analysis is performed through a finite element (FE) model. Differently from the analytical and FE simulations that can be found in the literature, the models presented in this work are entirely developed in threedimensional finite elasticity. Experiments are conducted with a device that allows the rubber specimens to undergo large axial deformations. For the first time, snapthrough is observed experimentally on rubber materials, showing good agreement with both theoretical and numerical results. Further insights on Eulerian buckling of the rubber specimens and its interaction with the snapthrough are given. A simple formulation to determine the critical load of the truss is presented and its accuracy is validated through experimental observation. Comparisons with a linear elasticity based approach demonstrate
that an accurate prediction of snapthrough and Eulerian buckling requires nonlinear formulations, such as the ones proposed in this work.
2021
 Snapthrough and Eulerian buckling of the von Mises truss
[Relazione in Atti di Convegno]
Pelliciari, Matteo; Falope, FEDERICO OYEDEJI; Lanzoni, Luca; Tarantino, Angelo Marcello
abstract
2021
 Snapthrough of a bistable truss in finite elasticity
[Relazione in Atti di Convegno]
Pelliciari, M.; Falope, F. O.; Lanzoni, L.; Tarantino, A. M.
abstract
2021
 Thermal conductivity of solids with coalescing spherical pores
[Abstract in Atti di Convegno]
Lanzoni, Luca; Radi, Enrico; Sevostianov, Igor
abstract
The overall thermal properties of media containing insulating cylindrical inhomogeneities has been addressed recently in [1] making reference to a 2D layout. There, the cross section of the fibers is formed by two intersecting circles to simulate a variety of nonconductive fibers (e.g. electrospinned polystyrene fibers). On the other hand, intersecting circles is a relevant layout to assess the physical properties of a variety of porous materials (e.g. Gasar metals) during the processes of pore coalescence and growth. In this work we extend the analysis addressed in [1] to a 3D framework by considering the effect of insulating inhomogeneities having the shape of intersecting spheres. The analysis aims at assessing the secondorder resistivity contribution tensor, which provides the corrective temperature gradient induced by the volume V * of the inhomogeneity over the reference volume V of the background material subjected the a remotely applied heat flux q. Owing to the geometric setting, reference is made to toroidal coordinates and Mehler–Fock transforms are used to represents the perturbation temperature field due to the inhomogeneity [2]. As remarked in [3] for coalescing spheres having the same diameter, the components of tensor R display a nonmonotonic trend varying the distance between their centers. In particular, unlike what is observed for spheroids, the stationary values of the components of tensor R occur when spherical pores are slightly intersecting.
2020
 A cohesive FE model for simulating the cracking/debonding pattern of composite NSCHPFRC/UHPFRC members
[Articolo su rivista]
Savino, Vincenzo; Lanzoni, Luca; Tarantino, Angelo Marcello; Viviani, Marco
abstract
The aim of this work is to propose to practitioners a simple cohesive FiniteElement model able to simulate the cracking/debonding pattern of retrofitted concrete elements, in particular NormalStrengthConcrete members (slabs, bridge decks, pavements) rehabilitated by applying a layer of HighPerformance or UltraHighPerformance FiberReinforcedConcrete as overlay. The interface was modeled with a proper nonlinear cohesive law which couples mode I (tensioncrack) with mode II (shearslip) behaviors. The input parameters of the FE simulation were provided by a new bond test which reproduces a realistic condition of cracking/debonding pattern. The FE simulations were accomplished by varying the overlay materials and the moisture levels of the substrate surface prior to overlay, since findings about their influence on the bond performances are still controversial. The proposed FE model proved to effectively predict the bond failure of composite NSCHPFRC/UHPFRC members.
2020
 A cohesive model to predict the loading bond capacity of concrete structures repaired/reinforced with HPFRC/UHPFRC and stressed to mixed mode
[Articolo su rivista]
Savino, Vincenzo; Lanzoni, Luca; Tarantino, Marcello; Viviani, Marco
abstract
The risk of cracking/debonding of a cement overlay used to repair or strengthen an existing structure is still a key issue. Current bond test methods are not designed to measure the combined effect of peeling (mode I) and shear (mode.II) on the interface. A few existing models propose theoretical approaches to predict that, but they were fitted on specific cases and lack in generality. In addition, controversial opinions about the influence of both the moisture level of the substrate surface prior to the application of the overlay and properties of the latter on the loading bond capacity call for further investigations. In this work, a cohesive model is developed to predict the loading bond capacity of an existing concrete structure overlaid by a layer of HPFRC/UHPFRC. Different bond tests were specifically designed for calibrating the cohesive parameters employed into the model, which also takes into account the type of the overlay used and the moisture conditioning level. An experimental campaign
confirmed the reliability of the predictions of the proposed theoretical model.
2020
 Buckling of a Timoshenko beam bonded to an elastic halfplane: Effects of sharp and smooth beam edges
[Articolo su rivista]
Falope, FEDERICO OYEDEJI; Lanzoni, Luca; Radi, Enrico
abstract
The problem of a compressed Timoshenko beam of finite length in frictionless and bilateral contact with an elastic halfplane is investigated here. The problem formulation leads to an integrodifferential equation which can be transformed into an algebraic system by expanding the rotation of the beam cross sections in series of Chebyshev polynomials. An eigenvalue problem is then obtained, whose solution provides the buckling loads of the beam and, in turn, the corresponding buckling mode shapes. Beams with sharp or smooth edges are considered in detail, founding relevant differences. In particular, it is proofed that beams with smooth edges cannot exhibit a rigidbody buckling mode. A characteristic value of the stiffness ratio dimensionless parameter has been found for sharp edges, under which without loss of reliability, an analytic buckling load formula is provided. Finally, in agreement with the Galin solution for the rigid flat punch on a halfplane, a simple relation between the halfplane elastic modulus and the Winkler soil constant is found. Thus, a straightforward formula predicting the buckling loads of high stiff beams resting on elastic compliant substrates is proposed.
2020
 Dispositivo smorzatore assiale ad elastomeri
[Brevetto]
Falope, FEDERICO OYEDEJI; Pelliciari, Matteo; Lanzoni, Luca; Tarantino, Angelo Marcello; Salardi, Enrico
abstract
2020
 Effect of spherical pores coalescence on the overall conductivity of a material
[Articolo su rivista]
Lanzoni, L.; Radi, E.; Sevostianov, I.
abstract
The problem about steadystate temperature distribution in a homogeneous isotropic medium containing a pore or an insulating inhomogeneity formed by two coalesced spheres of the same radius, under arbitrarily oriented uniform heat flux, is solved analytically. The limiting case of two touching spheres is analyzed separately. The solution is obtained in the form of converged integrals that can be calculated using GaussLaguerre quadrature rule. The temperature on the inhomogeneity’s surface is used to determine components of the resistivity contribution tensor for the insulating inhomogeneity of the mentioned shape. An interesting observation is that the extreme values of these components are achieved when the spheres are already slightly coalesced
2020
 FE Analyses of Hyperelastic Solids under Large Bending: The Role of the Searle Parameter and Eulerian Slenderness
[Articolo su rivista]
Falope, Federico; Lanzoni, Luca; Tarantino, Marcello
abstract
A theoretical model concerning the finite bending of a prismatic hyperelastic solid has been recently proposed. Such a model provides the 3D kinematics and the stress field, taking into account the anticlastic effects arising in the transverse cross sections also. That model has been used later to extend the Elastica in the framework of finite elasticity. In the present work, Finite Element (FE) analyses of some basic structural systems subjected to finite bending have been carried out and the results have been compared with those provided by the theoretical model performed previously. In the theoretical formulation, the governing equation is the nonlinear local relationship between the bending moment and the curvature of the longitudinal axis of the bent beam. Such a relation has been provided in dimensionless form as a function of the Mooney–Rivlin constitutive constants and two kinematic dimensionless parameters termed Eulerian slenderness and compactness index of the cross section. Such parameters take relevance as they are involved in the wellknown Searle parameter for bent solids. Two significant study cases have been investigated in detail. The results point out that the theoretical model leads to reliable results provided that the Eulerian slenderness and the compactness index of the cross sections do not exceed fixed threshold values.
2020
 Mechanics of highflexible beams under live loads
[Articolo su rivista]
Lanzoni, Luca; Tarantino, Angelo Marcello; Angelo, Marcello
abstract
In this paper the mathematical formulation of the equilibrium problem of highflexible beams in the framework of fully nonlinear structural mechanics is presented. The analysis is based on the recent model proposed by L. Lanzoni and A.M. Tarantino: The bending of beams in finite elasticity in J. Elasticity (2019) doi:10.1007/s10659019097468 2019. In this model the complete threedimensional kinematics of the beam is taken into account, both deformations and displacements are considered large and a nonlinear constitutive law in assumed. After having illustrated and discussed the peculiar mechanical aspects of this special class of structures, the criteria and methods of analysis have been addressed. A classification of the structures based on the degree of kinematic constraints has been proposed, distinguishing between isogeometric and hypergeometric structures. External static loads dependent on deformation (live loads) are also considered. The governing equations are derived on the basis of a momentcurvature relationship obtained in L. Lanzoni and A.M. Tarantino: The bending of beams in finite elasticity in J. Elasticity (2019) doi:10.1007/s10659019097468 2019. The governing equations take the form of a highly nonlinear coupled system of equations in integral form, which is solved through an iterative numerical procedure. Finally, the proposed analysis is applied to some popular structural systems subjected to dead and live loads. The results are compared and discussed.
2020
 Shotearth for sustainable constructions
[Articolo su rivista]
Curto, Andrea; Lanzoni, L; Tarantino, Am; Viviani, Marco
abstract
Earth has been used worldwide as a building material for centuries and it is still one of the most used construction materials. In many countries the excavated soil is becoming one of the largest construction waste and its disposal is costly and problematic. For this reason, there is a rising interest in employing the excavated soil directly in field, possibly as an added value construction material. In this paper a new type of rammed earth is presented. This new material is based on the shotcrete technology and has been named shotearth. A mix of stabilized soil, aggregates and water is consolidated by high speed projection rather than by mechanical compaction to obtain both structural and nonstructural elements. The first characterization of the physical properties of this material has shown the great potential of this technology
2020
 The Bending of Beams in Finite Elasticity
[Articolo su rivista]
Lanzoni, L.; Tarantino, A. M.
abstract
In this paper the analysis for the anticlastic bending under constant curvature of nonlinear solids and beams, presented by Lanzoni, Tarantino (J. Elast. 131:137–170,2018), is extended and further developed for the class of slender beams. Following a semiinverse
approach, the problem is studied by a threedimensional kinematic model for the longitudinal inflexion, which is based on the hypothesis that cross sections deform preserving their planarity. A compressible MooneyRivlin law is assumed for the stored energy function and from the equilibrium equations, the free parameter of the kinematic model is computed. Thus, taking into account the threedimensionality of the beam, explicit formulae for the displacement field, the stretches and stresses in every point of the body, following both Lagrangian and Eulerian description, are derived. Subsequently, slender beams under variable curvature were examined, focusing on the local determination of the curvature and bending moment along the deformed beam axis. The governing equations take the form of a coupled system of three equations in integral form, which is solved numerically. The proposed analysis allows to study a very wide class of equilibrium problems for nonlinear beams under different restraint conditions and subject to generic external load systems. By way of example, the Euler beam and a cantilever beam loaded by a dead or live (follower) concentrated force applied at the free end have been considered, showing the shape assumed by the beam as the load multiplier increases.
2019
 An extended model to predict the compressive, tensile and flexural strengths of HPFRCs and UHPFRCs: Definition and experimental validation
[Articolo su rivista]
Savino, Vincenzo; Lanzoni, Luca; Tarantino, Angelo Marcello; Viviani, Marco
abstract
High manufacturing costs of UHPFRC and expensive and timeconsuming tests performed to understand the mechanical response under loading restrict still its wider applications in thefield of the structural engineering. Predictive models can be useful to reduce the number of requested tests and to optimize the amount of compounds of the mixture, for example detecting the minimal dosage offibers necessary to attain a given tensile strength and toughness as well. Currently, not many predictive models do exist and one of the most recent, developed in order to estimate the compressive and tensile responses of HPFRCs, was not notably suitable for UHPFRCs. The main purpose of this work concerns the extension of such a model, in order to predict the mechanical response (inflexion as well) of a given HPFRC/UHPFRC for any change of matrix and fiber properties. Theoretical results were compared with experimental data, thus conforming some shortcomings of the previous model. Once the matrix andfiber properties of a marked UHPFRC were selected, the extended model was used to predict the tensile andflexural bending responses of a full scale UHPFRC structural beam, showing good agreement with the experimental results.
2019
 Bending device and anticlastic surface measurement of solids under large deformations and displacements
[Articolo su rivista]
Falope, F. O.; Lanzoni, L.; Tarantino, A. M.
abstract
Large bending of elastic bodies gives rise to significant transverse effects. Based on a recent theoretical model in the context of finite elasticity, both the longitudinal and anticlastic curvatures in bent solids under large deformation and displacement can be accurately assessed. In order to experimentally investigate the anticlastic deformation induced by large inflexion and corroborate the theoretical predictions, a properly designed mechanical bending device is here proposed. By imposing a rotation at the ends of the sample, both the longitudinal and anticlastic curvatures are measured by DIC (digital image correlation) monitoring instrumentation and compared with the theoretical results, finding good agreement. Compact analytical formulae for assessing the radii of curvature within the thickness of the sample are provided. Conversely to existing studies of the anticlastic surface induced by infinitesimal bending, the present analysis takes into account large throughtothickness curvature variations, whose knowledg can plays a key role for a wide class of mechanical applications.
2019
 Bending of beams in finite elasticity and some applications
[Abstract in Atti di Convegno]
Lanzoni, Luca; Tarantino, Angelo Marcello
abstract
The 2D Rivlin solution concerning the finite bending of a prismatic solid has been recently extended by accounting for the complete 3D displacement field [1]. In particular, the relationship between the principal and transverse (anticlastic) deformation of a bent solid has been investigated, founding the coupling relationships among three kinematic parameters which govern the problem. Later, based on the formulation reported in [1], and making reference to a (hyper)elastic material, the formulation has been extended to slender beams by introducing some simplifying assumptions [2]. This leads to a challenging relation between the external bending moment m and the curvature R01 of the longitudinal axis, which involves both the constitutive and geometric parameters of the beam. This relation can be viewed as a generalization of the Elastica [3].
However, such a relationship can be simplified through a series expansion, thus obtaining a reliable momentcurvature relation as follows [4], being a, b, c the constitutive parameters involved in the stored energy function according to a compressible MooneyRivlin material, whereas r denotes the anticlastic radius of the cross section [1]. In eqn (1)1 the radius of curvature R0 depends on the curvilinear abscissa s describing the beam axis in its deformed configuration. The rotation of the beam cross section follows from the derivative of the curvature with respect abscissa s, i.e. ’(s) = R01(s). Thus, the axial and vertical components of the displacement field and the rotation of the beam cross section are found to be coupled in a set of three equations in integral form, which is handled in an iterative procedure in order to analyse elastic structures exhibiting deformations and displacements both large.
Some basic structural schemes under both dead and live loads are here investigated, thus assessing the deformed configuration and the arising internal forces into the beam. It is found that the magnitude of the external loads strongly affects the qualitative distribution of the axial and shear forces and the bending moment in the inflexed beam, giving rise to a solution which completely differs to that corresponding to infinitesimal strains and small displacements.
2019
 Effect Of Pair Coalescence Of Circular Pores On The Overall Elastic Properties
[Articolo su rivista]
Lanzoni, L.; Radi, E.; Sevostianov, I.
abstract
The paper focuses on the effect of the pair coalescence of circular pores on the overall elastic properties. An analytic solution for the stress and displacement fields in an infinite elastic medium, containing cylindrical pore with the crosssection formed by two circles, and subjected to remotely applied uniform stresses is obtained. The displacement field on the surface of the pore is then determined as a function of the geometrical parameters. This result is used to calculate compliance contribution tensor for the pore and to evaluate effective elastic properties of a material containing multiple pores of such a shape.
2019
 Effective elastic properties of media containing coalescing holes
[Abstract in Atti di Convegno]
Lanzoni, Luca; Radi, Enrico; Sevostianov, Igor
abstract
A recent study about the temperature and heat flux distributions around two nonconductive (separate or intersecting) circular holes in a plane system recently appeared in Literature [1]. These results have been used to construct the secondrank resistivity contribution tensor which allows assessing the effective thermal properties of a composite including circular inhomogeneities.
Here, that study is extended to assess the overall elastic properties of an isotropic elastic matrix with two separate circular cavities or a cavity obtained by the union of two circles of generally different diameters (Figure 1). The problem is formulated in terms of stress functions expressed in Fourier series or Fourier transforms. Reference is made to bipolar cylindrical coordinates [2]. Once the displacement field u has been calculated, the extra strain due to the inhomogeneity is assessed according to (1), being n the normal vector and V the volume reference. Finally, the extra strain is used to assess the fourthrank compliance contribution tensor varying the size of the circular arcs.
2019
 Finite bending of beams with anticlastic effect: analytical model, experimental test and FE modeling
[Abstract in Atti di Convegno]
Falope, FEDERICO OYEDEJI; Lanzoni, Luca; Tarantino, Angelo Marcello
abstract
A recent model of a bent solid in finite elasticity appears in Literature [1]. Making reference to a compressible MooneyRivlin material, such a model is able to describe properly the anticlastic effect arising in a bent beam made of a rubberlike material. An experimental device is here presented (see Figure 1) aimed at simulating pure bending. In particular, the device lets the specimen free to exhibit its own elastic retaining force. Accordingly, the bent sample assumes the shape of an arc of circumference. With the aid of a DIC optical monitoring system, the experimental displacement field is acquired during the deformation process varying the angles imposed at the final beam cross sections. For different rubber specimens, based on a theoretical model [2], both compression and tensile tests have been performed in order to properly characterize the constitutive parameters. Once the
constitutive parameters have been found, by means of nonlinear fitting experimental data, a FE model has been carried out in order to reproduce the experimental test. A good agreement is found among analytical, experimental and numerical results, thus showing the reliability of the proposed experimental device together with the consistency of the basic hypotheses of the theoretical model.
2019
 Modèle prédictif visant à optimiser les composants du BFUP en réponseaux exigences d’application
[Abstract in Atti di Convegno]
Savino, Vincenzo; Lanzoni, Luca; Tarantino, Angelo Marcello; Viviani, Marco
abstract
Tous les matériaux de construction doivent être caractérisés préalablement, pour qu’ils répondent aux exigences demandées par les concepteurs. Pour le Béton Fibré Ultra Performant (BFUP), l’innovation continue de ses composants, due aux progrès technologiques, en modifie les propriétés mécaniques en comparaison à la version précédente du même produit. Cela demande de nouveaux essais de formulation du mélange visant à atteindre les performances rigoureuses demandées par les concepteurs. En outre, le coût élevé de production, principalement imputable à la présence des fibres métalliques dans le mélange, limite une exploitation plus étendue d’un tel produit sur le marché. Dans cet article, un modèle prédictif de résistance a été développé pour détecter le type et la quantité minimale de fibres à ajouter dans une matrice cimentaire donnée, afin de satisfaire les exigences de performances demandées et de réduire le nombre de matériaux différents à tester, en guidant le choix d’optimisation de la composition du mélange. Le modèle, validé par une étude expérimentale, a enfinété appliqué dans un cas pratique.
2019
 Pullout modelling of viscoelastic synthetic fibres for cementitious composites
[Articolo su rivista]
Sorzia, Andrea; Lanzoni, Luca; Radi, E
abstract
The problem of the pullout of a viscoelastic synthetic fibre embedded in a cementitious matrix and subjected to an external timedependent axial load is considered in the present work. A 1D phenomenological model able to simulate the contribution of viscoelastic relaxation as well as the hardening behavior due to abrasion phenomena during slippage is developed. The cement matrix compliance is neglected with respect to the fibre elongation. The interfacial shear stress between the fibre and the surrounding matrix is assumed to depend on the slippage distance through a second degree polynomial law, thus involving three constitutive parameters. Two distinct phases are recognized: An earlier debonding stage followed by the effective fibre pullout process. Two different creep functions have been assumed for modelling the viscous response of polymeric fibres: A function based on the fractionexponential Rabotnov operator and a classical exponential model. Identification of the governing constitutive parameters allows obtaining the relation between the external strain and the axial displacement, which has been compared with experimental results provided by pullout tests both on plain and treated fibres, finding a good agreement. It is shown that the proposed approach can predict the whole pullout process of discrete synthetic macrofibres.
2019
 The Bending Theory of Fully Nonlinear Beams
[Monografia/Trattato scientifico]
Tarantino, A. M.; Lanzoni, L.; Falope, F. O.
abstract
This book presents the bending theory of hyperelastic beams in the context of finite elasticity. The main difficulties in addressing this issue are due to its fully nonlinear framework, which makes no assumptions regarding the size of the deformation and displacement fields. Despite the complexity of its mathematical formulation, the inflexion problem of nonlinear beams is frequently used in practice, and has numerous applications in the industrial, mechanical and civil sectors. Adopting a semiinverse approach, the book formulates a threedimensional kinematic model in which the longitudinal bending is accompanied by the transversal deformation of crosssections. The results provided by the theoretical model are subsequently compared with those of numerical and experimental analyses. The numerical analysis is based on the finite element method (FEM), whereas a test equipment prototype was designed and fabricated for the experimental analysis. The experimental data was acquired using digital image correlation (DIC) instrumentation. These two further analyses serve to confirm the hypotheses underlying the theoretical model. In the book’s closing section, the analysis is generalized to the case of variable bending moment. The governing equations then take the form of a coupled system of three equations in integral form, which can be applied to a very wide class of equilibrium problems for nonlinear beams.
2019
 The bending of fully nonlinear beams. Theoretical, numerical and experimental analyses
[Articolo su rivista]
Falope, Federico; Lanzoni, Luca; Tarantino, Angelo Marcello
abstract
This paper deals with the equilibrium problem of fully nonlinear beams in bending by extending the model for the anticlastic flexion of solids recently proposed by Lanzoni and Tarantino (2018) in the context of finite elasticity. In the first part of the paper it
is shown, through a parametric analysis, that some geometrical parameters of the displacement field lose importance when slender beams are considered. Therefore, kinematics is reformulated and, subsequently, a fully nonlinear theory for the bending of
slender beams is developed. In detail, no hypothesis of smallness is introduced for the deformation and displacement fields, the constitutive law is considered nonlinear and the equilibrium is imposed in the deformed configuration. Explicit formulas are
obtained which describe the displacement fields of the inflexed beam, the stretches and the stresses for each point of the beam using both the Lagrangian and Eulerian descriptions. All these formulas are linearized by retrieving the classical formulae of the
infinitesimal bending theory of beams. In the second part of the paper the theoretical results are compared with those provided by numerical and experimental analyses developed for the same equilibrium problem with the aim of justify the hypotheses
underlying the theoretical model. The numerical model is based on the finite element (FE) method, whereas a test equipment prototype is designed and manufactured for the experimental analysis.
2018
 Double lap shear test on steel fabric reinforced cementitious matrix (SFRCM)
[Articolo su rivista]
Falope, F. O.; Lanzoni, L.; Tarantino, Angelo Marcello
abstract
The present work deals with the experimental characterization of the mechanical behaviour of a galvanized steel fabric reinforced cementitious matrix (SFRCM).
2018
 Effect of cylindrical fibers, with crosssections formed by two circular arcs, on the overall conductivity of a composite
[Articolo su rivista]
Lanzoni, L.; Radi, E.; Sevostianov, I.
abstract
An analytic solution for the steadystate temperature distribution in an infinite conductive medium, containing nonconductive fiber with the crosssection of irregular shape formed by two circles, and subjected to remotely applied uniform heat flux is obtained. The temperature flux on the surface of the inhomogeneity is then determined as a function of the geometrical parameters. This result is used to calculate resistivity contribution tensor for the fiber and to evaluate effective conductive properties of a material containing multiple inhomogeneities of this shape.
2018
 Effective properties of composites containing toroidal inhomogeneities
[Relazione in Atti di Convegno]
Radi, Enrico; Sevostianov, Igor; Lanzoni, Luca
abstract
The present work focuses on the problem of a rigid inhomogeneity of toroidal shape embedded in an elastic matrix. Inhomogeneities of this kind occur in both natural and manmade materials. Barium titanate nanotori are used as nonvolatile memory devices, transducers, optical modulators, sensors and possible energy storage in supercapacitors. Toroidal particles represent preferred morphology of Li2O2 deposition on porous carbon electrode in lithiumoxygen batteries. Polymeric “microdonuts” are used in bioengineering; toroidal shape of nanoparticles is preferred for microwave absorption properties of BaTiO3. Toroidal particles of SiO2 may form in a Cu matrix due to internal oxidation of a CuSi solidsolution polycrystal. Analytical modeling of materials with such microstructure has not been well developed. In the homogenization schemes, the inhomogeneities are usually assumed to be of ellipsoidal shape. This unrealistic assumption is responsible for insufficient linkage between micromechanics and materials science applications. While for 2D nonelliptical inhomogeneities many analytical and numerical results have been obtained, only a limited number of approximate estimates are available for nonellipsoidal 3D shapes. Asymptotic methods have been used in [1] to evaluate the contribution of a thin rigid toroidal inhomogeneity into overall stiffness. Eshelby tensor for a toroidal inclusion has been also derived by Onata. However, Eshelby tensor for nonellipsoidal inhomogeneities is irrelevant to the problem of effective properties of a heterogeneous material. The effective conductivity of a material containing toroidal insulating inhomogeneities has been addressed in [2].
We first consider a homogeneous elastic material, with isotropic stiffness tensor C0, containing a rigid inhomogeneity of volume V(1). The contribution of the inhomogeneity to the overall stress per representative volume V (the extra stress Δσ, as compared to the homogeneous matrix) is given by the fourthrank stiffness contribution tensor N, defined by the following relation
where ε ∞ is the remotely applied strain, n is the outward unit normal to the inhomogeneity surface S. To calculate the components of N, a displacement boundary value problem has been solved for 3D elastic space containing a rigid toroidal inhomogeneity.
2018
 Effects of toroidal inhomogeneities on the effective properties of a composite
[Relazione in Atti di Convegno]
Radi, E.; Lanzoni, L.; Sevostianov, I.
abstract
The present work focuses on the problem of rigid inhomogeneity of toroidal shape embedded in an elastic matrix. Inhomogeneities of this kind occur both in natural and manmade materials. Analytical modeling of materials with such microstructure has not been well developed. In the homogenization schemes, the inhomogeneities are usually assumed to be of ellipsoidal shape. This unrealistic assumption is largely responsible for insuffcient linkage between methods of micromechanics and materials science applications. While for 2D nonelliptical inhomogeneities many analytical and numerical results have been obtained, only a limited number of numerical results and approximate estimates are available for nonellipsoidal 3D shapes. Most of them are related to pores and cracks. The problem of the effective conductivity (thermal or electric) of a material containing toroidal insulating inhomogeneities has been addressed in a pèrevious work, where an analytic solution is presented for the steadystate temperature distribution in an infinite conductive medium containing an insulated toroidal inclusion, under uniform heat flux in an arbitrary direction. The temperature flux on the torus surface is then determined as a function of torus parameters. This result is then used to determine resistivity contribution tensor for the toroidal inhomogeneity and for calculation of effective conductive
properties of a material containing multiple inhomogeneities of this shape.
A general analytical solution is developed here for the problem of an infinite elastic medium containing a rigid toroidal inhomogeneity, under remotely applied uniform strain. The traction vector on the torus surface is determined as a function of torus parameters and remote strain components. The results are utilized to calculate the components of the fourthrank stiffness contribution tensor of the rigid toroidal inhomogeneity that are required for calculation of the overall elastic properties of a material containing multiple toroidal inhomogeneities. The analytical results are verified by comparison with FEM calculations.
2018
 Finite Anticlastic Bending of Hyperelastic Solids and Beams
[Articolo su rivista]
Lanzoni, Luca; Tarantino, Angelo Marcello
abstract
This paper deals with the equilibrium problem in nonlinear elasticity of hyperelastic solids under anticlastic bending. A threedimensional kinematic model, where the
longitudinal bending is accompanied by the transversal deformation of cross sections, is
formulated. Following a semiinverse approach, the displacement field prescribed by the
above kinematic model contains three unknown parameters. A Lagrangian analysis is performed and the compressible MooneyRivlin law is assumed for the stored energy function.
Once evaluated the PiolaKirchhoff stresses, the free parameters of the kinematic model are
determined by using the equilibrium equations and the boundary conditions. An Eulerian
analysis is then accomplished to evaluating stretches and stresses in the deformed configuration. Cauchy stress distributions are investigated and it is shown how, for wide ranges
of constitutive parameters, the obtained solution is quite accurate. The whole formulation
proposed for the finite anticlastic bending of hyperelastic solids is linearized by introducing the hypothesis of smallness of the displacement and strain fields. With this linearization
procedure, the classical solution for the infinitesimal bending of beams is fully recovered
2018
 Microstructural analysis and mechanical properties of concrete reinforced with polymer short ﬁbers
[Articolo su rivista]
Troﬁmov, Anton; Mishurova, Tatiana; Lanzoni, Luca; Radi, Enrico; Bruno, Giovanni; Sevostianov, Igor
abstract
The paper focuses on the development of a methodology for quantitative characterization of a concrete containing polymer ﬁbers and pores. Computed tomography (CT) characterization technique is used to provide input data for Finite Element Method (FEM) simulations and analytical modeling based on micromechanical homogenization via the compliance contribution tensor formalism. Effective elastic properties of reinforced concrete are obtained experimentally using compression testing, analytically in the framework of NonInteraction approximation and numerically performing direct FEM simulations on specimen with reconstructed microstructure. It is shown that CT produces results suitable for implementation in numerical and analytical models. The results of analytical and numerical modeling are in a good agreement with experimental measurements providing maximum discrepancy of ∼ 2.5%.
2018
 Modified hinged beam test on steel fabric reinforced cementitious matrix (SFRCM)
[Articolo su rivista]
Falope, F. O.; Lanzoni, L.; Tarantino, A. M.
abstract
An experimental campaign based on modied hinged beam test (MhBT) setup has been reported in the present study. The samples consist of two concrete blocks coupled by a proper hinge device and laminated with steel wire fabrics embedded in a cementitious mortar layer. Two kinds of fabrics, made of galvanized steel strands with dierent mesh spacing, have been used to reinforce the concrete joists. With the aid of a DIC monitoring system, slippage prole at the interface between the concrete support and the mortar laminate along the contact region has been assessed, together with the fracture opening. Force
vs slippage at the interface has been retrieved for the sampled tested according to the MhBT setup. With the aim to obtain predictive ultimate load design formulas, a novel classication of laminate here proposed will be argued and related to a MhBT design formula. The in influence of peel and shear stresses interaction on the ultimate strength of the system has been discussed in detail.
2018
 Overall elastic properties of a plate containing inhomogeneities of irregular shape
[Relazione in Atti di Convegno]
Lanzoni, L.; Radi, E.; Sevostianov, I.
abstract
The present work deals with the stiffness properties of an infinite 2D isotropic elastic system containing inhomogeneities having a circular contour. Starting from this general layout, the cases of a matrix with lenticular, perfectly circular, semicircular, “Cshaped” and thin straight inclusions can be obtained as limit cases. Owing to the geometry of the system, reference is made to bipolar cylindrical coordinates ( ), which are linked to the Cartesian ones (x1, x2) through the conformal map [2]. The effective elastic properties of the system is analytically investigated by introducing a fourthorder compliance contribution tensor H, which represents the effect induced by the inhomogeneity on the compliance of the system according to [1], being S the compliance tensor for the homogeneous elastic matrix and e the stress field. It is remarked that the last term in eq (1) denotes the correction acting on the strain field owing to the presence of the inclusions. The system without inhomogeneities and subjected to a remote stress field is considered first. The corresponding fundamental stress field (0) within the matrix does not accomplish the BCs at the contour of the inhomogeneities. Thus, following the Jeffery approach, an auxiliary stress field deduced by a biharmonic stress function in bipolar coordinates is introduced and tensor H is then evaluated by performing proper contour integrals involving the total stress distribution along the contours of the inclusions. The study allows evaluating the effective elastic properties of a wide class of inhomogeneous materials, with particular reference to composites reinforced with natural or synthetic fibres having optimized cross sections.
References
[1] Sevostianov, I., and Kachanov, M., “Explicit crossproperty correlations for anisotropic
twophase composite materials” Journal of the Mechanics and Physics of Solids, 50, 253282 (2002).
[2] Korn, G.A. and Korn, T.M., Mathematical handbook for scientists and engineers. Definitions, Theorems and Formulas for Reference and Review, Dover, New York (1968).
2018
 Overall thermal conductivity of fibre reinforced materials
[Abstract in Atti di Convegno]
Lanzoni, Luca; Radi, Enrico; Sevostianov, Igor
abstract
The overall thermal conductivity of composites involving cylindrical fibres of irregular shape is investigated in the present work. Isotropic and homogeneous thermal conductivity is assumed for both the matrix and fibre. The system consists of an infinite plate with an embedded fibre subjected to a remotely applied steady state heat flux q acting along a given
direction. Once the alteration of the heat flux and temperature field T due to the presence of the inclusion is assessed, the homogeneized thermal properties of the composite material can be computed following the procedure reported in [1].
As an example, the dimensionless temperature distribution Tk/Rq and heat flow q/q in an infinite with a nonconductive
circula fiber is sketched in Figure 1, being k the thermal conductivity of the matrix and R denotes the radius of the fiber.
The study extends the results reported in [2] performed for nonconductive inclusions accounting for the real thermal conductivity of the fibres. The analysis allows assessing the effective thermal properties of a fibre reinforced material based on fibres with cross section formed by circular arcs, as polystyrene, polyacrylonitrile and sisal fibres.
2018
 Safety Assessment of Historic Timber Structural Elements
[Articolo su rivista]
Barozzi, G.; Cosentino, N.; Lanzoni, L.; Tarantino, A. M.
abstract
Dealing with the safety assessment of existing buildings engineers often have to face the diagnosis of old timber structures. The current standards framework does not provide clear prescriptions about the evaluation of these kinds of structures, so the principal aim of this work is to outline an alternative methodology that leaves the concept of "Knowledge Level" and "Condence Factor", usually applied for existing buildings. An experimental campaign carried out on old timber joists supplied a sample of homogeneous data that
were the support to the theoretical reasoning.
2018
 Shafthub press fit subjected to couples and radial forces: analytical evaluation of the shafthub detachment loading
[Articolo su rivista]
Bertocchi, Enrico; Lanzoni, Luca; Mantovani, Sara; Radi, Enrico; Strozzi, Antonio
abstract
A shafthub press fit subjected to two nonaxisymmetric loading conditions is examined and the situation
of incipient detachment between the shaft and the hub is determined. The first condition consists of a
central radial load P applied to the hub, balanced by two lateral forces P=2 applied to the shaft at a
distance d from the hub lateral walls. In the second condition, a central couple C is applied to the hub,
and it is balanced by two lateral opposite loads withstood by the shaft at a distance d from the hub
lateral walls. The shafthub contact is modelled in terms of two elastic Timoshenko beams connected by
distributed elastic springs (Winkler foundation), whose constant is analytically evaluated. Based upon
this enhanced beamlike modelling, the loading inducing an undesired shafthub incipient detachment
is theoretically determined in terms of the shafthub geometry, of the initial shafthub interference, and
of the elastic constants. Finite element forecasts are presented to quantify the error of this beamlike
approximate analytical approach.
2018
 Shear deformable beams in contact with an elastic halfplane
[Abstract in Atti di Convegno]
Falope, F. O.; Lanzoni, L.; Radi, E.
abstract
The present work deals with the contact problem of a Timoshenko beam bonded to an elastic semiinfinite substrate under different loading conditions. The analysis allows investigating the effects induced by shear compliance of the beam, the stress intensity factors ad the beam edges as well as the singular nature of the interfacial stresses.
2018
 Simple and effective models to predict the compressive and tensile strength of HPFRC as the steel fiber content and type changes
[Articolo su rivista]
Savino, Vincenzo; Lanzoni, L.; Tarantino, A. M.; Viviani, M.
abstract
HPFRC/UHPC are today widely applied as repair and reinforcement materials for structures. One of the
drawback of commercial HPFRC/UHPC is that any modification of the matrixfibers mix design, due to the
market requirements, affects the mechanical properties of the hardened concrete and therefore the data obtained
testing the previous version of the concrete are useless. Prediction models that link the properties of bothfibers
and matrix to the performances of the hardened concrete are of great practical interest. This paper present a
simple and effective model to account for the effect offibers on the compressive and tensile strengths of HPFRCs
as the aspect ratio and volume offibers changes, extending the range of application of the few existing models.
2018
 Stress analysis around a tunnel in a gravitating poroelastic half plane
[Relazione in Atti di Convegno]
Lanzoni, Luca; Radi, Enrico; Nobili, Andrea
abstract
The present work deals with the mechanical behaviour of a circular tunnel embedded in a semiinfinite
poroelastic half plane under gravitational body forces. Owing to the geometric layout,
reference is made to bipolar cylindrical coordinates (, ) and symmetry occurs with respect to
coordinate. The fluid flux is assumed stationary, thus making the fluid pressure p a harmonic field, being Cn, Dn unkonwn arbitrary constants.
The problem is governed by the following Navier equation in terms of the displacement field the solid phase, where denotes the elastic shear modulus of the solid phase, g is the ground acceleration, e1 denotes the unit vector of the vertical axis, n is the porosity and the (real and positive) parameters and sw characterize completely the mechanical response of the poroelastic soil according to
the Bowen formalism [1]. A particular solution of eqn (2) is found in closed form by introducing a Helmholtz potential
for the displacement. However such a solution does not accomplish the BCs at the ring of the
tunnel and at the free surface of the half plane. Then, by following the Jeffery procedure [2], an
auxiliary Airy stress function is introduced that, added to the fundamental solution, allows
accomplish the BCs.
Two limit situations are considered at the ring of the tunnel. In particular, a given radial
pressure acting at the ring of the tunnel (Dirichlet BCs) and a given fluid flux across the contour of
the tunnel (Neumann BCs) have been considered [3]. The latter situation allows investigating the
effect of a tunnel having an impermeable surface embedded in a gravitating poroelastic soil.
Results in terms of fluid pressure and stress near the rim of the hole as well as at the free
surface of the half plane are analysed in detail varying both the geometric and constitutive
parameters of the system.
2018
 Stress and pressure fields around two wellbores in a poroelastic medium
[Articolo su rivista]
Lanzoni, Luca; Radi, Enrico; Nobili, Andrea
abstract
The problem of two circular wellbores of different size in a poroelastic medium is considered in the present work. The constitutive behaviour of the poroelastic medium is assumed to comply with the classical Biot model for isotropic porous materials infiltrated by compressible fluid. The wellbores are assumed infinitely long and the fluid flow is taken stationary, thus making it possible to perform a plane strain analysis. Owing to the geometrical layout of the system, bipolar cylindrical coordinates have been adopted. Three different sets of BCs on the pressure field and on the fluid flux have been considered, founding the corresponding forms of the pressure field. Based on Helmholtz representation, a displacement potential has been introduced, and the corresponding stress field in the poroelastic medium has been assessed. However, such a solution does not satisfy the BCs at the edges of the wells. Then, an auxiliary stress function, which allows accomplishing the BCs, is introduced, leading to the complete solution of the problem. The cases of two coaxial wellbores (eccentric annulus), a single hole bored in a poroelastic half plane and two intersecting holes have been considered also. The proposed approach allows evaluating the pore pressure and the stress and strain fields in the system varying the amplitude of the wells and the physical parameters of the porous material. In particular, the evaluation of the peak values of the stress components around the circular boreholes plays a key role in a variety of engineering contexts, with particular reference to the stability analysis of wellbores and tunnels and failure of vascular vessels in biological tissues.
2018
 Tensile constitutive behavior of high and ultrahigh performance fibrereinforcedconcretes
[Articolo su rivista]
Savino, Vincenzo; Lanzoni, L.; Tarantino, A. M.; Viviani, M.
abstract
High Performance FibreReinforcedCementComposites and UltraHigh Performance FibreReinforcedConcretes, also named HPFRCCs and UHPFRCs respectively, are today widely used as repair and strengthening existing structures, such as bridge decks, pavements, piers etc. Simple test methods to characterize its mechanical behavior are requested, in order to ensure that the product meets the designer’s requirements, especially in term of tensile behavior. Various test methods are available, even though a proper correlation between direct and indirect tensile (e.g. flexural) tests is needed. In this paper a model based on the ‘‘Composite Material Theory” (CMT) was developed to predict the flexural behavior of three commercialized SFRCs once the direct tensile strength is measured. A good agreement was found between experimental results and the values predicted by the model.
2017
 A WienerHopf System of Equations in the SteadyState Propagation of a Rectilinear Crack in an Infinite Elastic Plate
[Relazione in Atti di Convegno]
Nobili, Andrea; Radi, Enrico; Lanzoni, Luca
abstract
A WienerHopf system of functional equations is shown to govern the steadystate propagation of a semiinfinite rectilinear crack in an infinite elastic Kirchhoff–Love plate. Solution is presented in terms of Fourier transforms via kernel factorization
2017
 Effective thermal properties of fibre reinforced materials
[Relazione in Atti di Convegno]
Lanzoni, L.; Radi, E.; Tarantino, A. M.
abstract
The thermal behaviour of an elastic matrix reinforced with synthetic micro or macro fibres subjected to a constant heat flow is investigated in the present work. Steadystate condition for the heat flux is considered and isotropic thermal conductivity for both the matrix and fibres is assumed. Owing to the geometry of the system, reference is made to bipolar cylindrical coordinates.
Various boundary conditions can be considered on the contours of the fibres. In particular, for a matrix reinforced with two fibres taken as insulated inclusions, a vanishing heat flow across the contour of the fibres must be imposed.
After the temperature field has benn determined analytically, a homogeneization procedure is performed in order to find the equivalent thermal properties of the fibre reinforced composite material.
2017
 Flexural edge waves generated by steadystate propagation of a loaded rectilinear crack in an elastically supported thin plate
[Articolo su rivista]
Nobili, Andrea; Radi, Enrico; Lanzoni, Luca
abstract
The problem of a rectilinear crack propagating at constant speed in an elastically supported thin plate and acted upon by an equally moving load is considered. The fullfield solution is obtained and the spotlight is set on flexural edge wave generation.
Below the critical speed for the appearance of travelling waves, a threshold speed is met which marks the transformation of decaying edge waves into edge waves propagating along the crack and dying away from it. Yet, besides these, and for any propagation speed, a pair of localized edge waves, which rapidly decay behind the crack tip, is also shown to exist. These waves are characterized by a novel dispersion relation and fade off from the crack line in an oscillatory manner, whence they play an important role in the far field behaviour. Dynamic stress intensity factors are obtained and, for speed close to the critical speed, they show a resonant behaviour which expresses the most efficient way to channel external work into the crack. Indeed, this
behaviour is justified through energy considerations regarding the work of the applied load and the energy release rate. Results might be useful in a wide array of applications, ranging from fracturing and machining to acoustic emission and defect detection.
2017
 Shafthub press fit subjected to bending couples: Analytical evaluation of the shafthub detachment couple
[Articolo su rivista]
Radi, Enrico; Lanzoni, Luca; Strozzi, Antonio; Bertocchi, Enrico
abstract
A mathematical modelling of a shafthub pressfit subjected to bending couples applied to the shaft extremities is developed, and the value of the bending couple inducing an un desired shafthub incipient detachment is analytically determined. The shafthub contact is modelled in terms of two elastic Timoshenko beams connected by a distributed elastic spring, whose stiffness is analytically evaluated. Two models of the distributed spring are considered. The first model expresses the combined deformability of both the shaft and the hub cross sections. The second model accounts for the stiffening effect exerted by the shaft portion protruding from the hub on the adjacent shaft part that is in contact with the hub, and, consequently, it assumes only a rigid body motion of the shaft cross section, thus neglecting its deformability. Based upon this beamlike model, the bending couple producing the incipient detach ment between the shaft and the hub is theoretically determined in term of the shafthub geometry, of the initial shafthub interference, and of the elastic constants. Comparisons with selected Finite Element (FE) forecasts indicate that the first modelling produces an incipient detachment couple that appreciably overrates the FE forecasts, whereas the sec ond modelling lowers the error down to technically acceptable predictions.
2016
 A coupled FEBIE model for the static analysis of Timoshenko beams bonded to an orthotropic elastic halfplane
[Articolo su rivista]
Tezzon, Enrico; Tullini, Nerio; Lanzoni, Luca
abstract
Interface displacements, surface tractions and stresses of a flexible beam bonded to an elastic orthotropic halfplane are analysed by means of a Finite ElementBoundary Integral Equation (FEBIE) method. Numerical results are obtained by using lockingfree shear deformable beams and piecewise constant interfacial reactions. Making use of the generalised Green's function for the halfplane, the mechanical behaviour of fully bonded or detached beams subjected to force, couple or thermal load is investigated. The special cases of a beam in bilateral frictionless contact with the halfplane and a beam having a vanishing bending rigidity (thin film) are considered also. In particular, the maximum bending moment of beams subjected to a vertical point force are compared with some closedform solutions of the contact problem of a rigid indenter and with the solution of an infinite EulerâBernoulli beam in bilateral frictionless contact with an isotropic substrate. The research that led to the present paper was partially supported by a grant of the group GNFM of INdAM.
2016
 A loaded Timoshenko beam bonded to an elastic half plane
[Articolo su rivista]
Lanzoni, Luca; Radi, Enrico
abstract
The contact problem of a Timoshenko beam of finite length loaded by concentrated forces and couples and perfectly bonded to a homogeneous elastic and isotropic half plane is considered in the present work. The study is aimed to investigate the effects induced by shear deformation of the beam on the contact stresses arising at the interface between the beam and the underlying half plane. The asymptotic analysis of the stress field at the beam edges and in the neighborhood of the loaded section of the beam allows us to characterize the singular nature of the peeling and shear stresses. The problem is formulated by imposing the strain compatibility condition between the beam and the half plane, thus leading to a system of two singular integral equations with Cauchy kernel. The unknown interfacial stresses are expanded in series of Jacobi orthogonal polynomials displaying complex singularity. This approach allows us to handle the oscillatory singularity and to reduce the integral equations to a linear algebraic system of equations for the unknown coefficients of the interfacial stresses, which is solved through a method of collocation. The interfacial peeling and shear stresses and, in turn, the displacement field along the contact region have been calculated under various loading conditions acting on the beam. The internal forces and moments along the beam have been evaluated varying the shear and flexural stiffness of the beam. The complex stress intensity factors and the strength of the stress singularities have been assessed in detail.
2016
 A simple nonlinear model to simulate the localized necking and neck propagation
[Articolo su rivista]
Lanzoni, Luca; Tarantino, Angelo Marcello
abstract
This paper deals with the equilibrium problem in nonlinear dissipative inelasticity of damaged bodies subject to uniaxial loading and its main purpose is to show the interesting potentialities offered by the damage theory in modeling the necking and neck propagation phenomena in polymeric materials. In detail, the proposed mechanical model is a twophase system, with the same constitutive law but with different levels of damage for each phase. Despite its simplicity, it is shown that the model can straightforwardly reproduce the overall load–elongation curve provided by experimental tensile tests by involving only five parameters of clear physical meaning.
2016
 Concrete beams stiffened by polymerbased mortar layers: experimental investigation and modelling
[Articolo su rivista]
Lanzoni, Luca; Soragni, Marco; Tarantino, Angelo Marcello; Viviani, M.
abstract
In the present work, the main results provided by an experimental investigation, assessing the mechanical performances of concrete elements stiffened by a single or more layers of different kinds of polymer modified cementitious repair mortar, are presented. The study is aimed in order to investigate the failure mechanism occurring in the samples under bending loading. In particular, the experimental investigation allows checking if the collapse mechanism is driven by delamination occurring along the interface among the overlays or by cracks propagating from the tensile region to the compressive zone, as it occurs in a typical failure mechanism driven by flexure. Thirtyeight precast and prestressed concrete samples were realized and cured to simulate loadbearing concrete ceiling beams widely employed as floor systems for residential buildings. After curing, the samples were subjected to threepoint loading bending tests in order to evaluate the mechanical response of the specimens in terms of load vs. midspan transverse dis placement. Through the experimental tests, the crack initiation and propagation during the bending load ing have been also investigated. Simplified finite element (FE) models were performed to properly reproduce the actual response of ceiling beams under nonsymmetric loading bending. It is shown that the proposed FE model can be straightforwardly used to predict the behavior of concrete beams stiffened by polymerbased repair mortar layers.
2016
 Failure mechanism of FRC slabs on nonlocal ground
[Articolo su rivista]
Lanzoni, Luca; Nobili, Andrea; Radi, Enrico; Sorzia, Andrea
abstract
The present work deals with the mechanical behavior of a large FRC slab bilaterally supported by a nonlocal soil. The slab is modelled as a ductile Kirchhoff plate laying on a twoparameter elastic and transversally loaded by a uniform
pressure applied on a circular area, thus making the problem axisymmetric. This layout covers a wide array of practical applications of fiber reinforced concrete in structural and civil engineering related to the assessment of the load carrying capacity of industrial floors, roads, airfield pavements and building foundations. The problem is governed by a fourth
order linear ODE with variable coefficients, whose solution has been obtained in power series by using the Frobenius method. The analysis allows us to evaluate the influence of the size of the loaded area and the relative stiffness of the slab/subgrade system on the collapse mechanism and the corresponding load carrying capacity, as well as on the distributions of displacement, rotation, bending moments, shear force and contact pressure at the onset of collapse
2016
 Modeling and simulation of trapping mechanisms of granular media in space
[Relazione in Atti di Convegno]
Quadrelli, M. B.; Ius, P.; Lanzoni, L.
abstract
This paper describes the modeling and simulation of trapped granular media, within the context of the Granular Imager project. We describe the physics of trapped granular media in space, and the methodologies used to stably confine and shape such a medium using electromagnetic fields. The numerical models have also been validated with results in the literature, obtaining excellent agreement. The results of the numerical tests indicate that it is possible, with structural arrangements of rings and plates at different levels of electrostatic potential, to stably confine one or more charged particles, when driven by voltages that can be modulated in time and space.
2016
 On the effect of the backup plate stiffness on the brittle failure of a ceramic armor
[Articolo su rivista]
Nobili, Andrea; Radi, Enrico; Lanzoni, Luca
abstract
The present investigation enquires the role of the backup plate mechanical properties in the brittle failure of a ceramic tile. It provides a fullfield solution for the elastostatic problem of an infinite Kirchhoff plate containing a semiinfinite rectilinear crack (the tile) resting on a twoparameter elastic foundation (the backup plate) and subjected to general transverse loading condition.
The backup plate is modeled as a weakly nonlocal (Pasternaktype) foundation, which reduces to the familiar local (Winkler) model once the Pasternak modulus is set to zero. The same governing equations are obtained for a curved plate (shell) subjected to inplane equibiaxial loading.
Fourier transforms and the WienerHopf technique are employed. The solution is obtained for the case when the Pasternak modulus is greater than the Winkler modulus.
Superposition and a two step procedure are employed: first, an infinite uncracked plate subjected to general loading is considered, then the bending moment and shearing force distribution acting along the crack line is adopted as the (continuous) loading condition to be fed in the solution for the cracked plate.
Results are obtained as a function of the ratio of the Pasternak over the Winkler foundation stiffness times the tile flexural rigidity. It is established that the elastic foundation significantly affects the mechanical behavior of elastic plate. In particular, the Winkler model substantially underestimates the stress condition. Stress intensity factors are determined and they are employed as a guideline for increasing the composite toughness. The analytical solution presented in this paper may serve as a benchmark for a more refined numerical analysis.
2016
 Steady state propagation of a rectilinear crack in a thin elastic plate supported by a Winkler elastic foundation
[Relazione in Atti di Convegno]
Nobili, Andrea; Radi, Enrico; Lanzoni, Luca
abstract
We consider steady state propagation of a rectilinear crack in a infinite thin elastic Kirchhoff plate bilaterally supported by an elastic Winkler foundation. The crack flanks are subjected to a continuous (between the flanks) harmonic load. The problem's governing equation features the biharmonic operator together with a curvature (along the crack) term. Through application of the Fourier transforms to the even/odd part of the problem, a pair of inhomogenenous uncoupled WeinerHopf equations is met. Solution is obtained through numeric factorization
of the kernel function. The fullfield solution is given, together with conditions on the energy radiation. The special case of stationary crack is also retrieved.
2016
 Stress and pore pressure fields around two boreholes in a poroelastic medium
[Relazione in Atti di Convegno]
Lanzoni, Luca; Nobili, Andrea; Radi, Enrico
abstract
We calculate the stress and pore pressure field around two circular holes in a poroelastic fluidsaturated media
2016
 Thin film bonded to elastic orthotropic substrate under thermal loading
[Articolo su rivista]
Falope, FEDERICO OYEDEJI; Lanzoni, Luca; Radi, Enrico; Tarantino, Angelo Marcello
abstract
The problem of thin elastic films bonded on an elastic orthotropic substrate under thermal load is investigated in this work. Differently from past studies on the same topic, the effects induced by anisotropic behavior of the elastic substrate will be taken into account. Particular attention will also be paid to the determination of the displacement and stress fields induced by thermal loading. In particular, it is assumed that the thin films are deposed on the substrate at high temperature, and then the mismatch occurring during the cooling process, due to the difference between the thermal expansion coefficients of the two materials, is responsible for the permanent deformation assumed by the system. This phenomenon can be exploited for realizing a crystalline undulator. To this aim, the permanent deformation must be optimized in order to encourage the channeling phenomenon. By imposing equilibrium conditions and perfect adhesion between the film and the substrate, a singular integral equation is derived. A closedform solution is achieved by expanding the interfacial shear stress fields in Chebyshev series. The unknown coefficients in the series expansion are then determined by transforming the integral equation into an infinite algebraic system.
2015
 Analytical modelling of the pullout behavior of synthetic fibres treated with nanosilica
[Relazione in Atti di Convegno]
Radi, Enrico; Lanzoni, Luca; Sorzia, Andrea
abstract
An accurate onedimensional analytical model for simulating the pullout process of synthetic fibres from a cement matrix is proposed in the present study in order to shed light on the ductile behavior exhibited by Fibre Reinforced Concrete (FRC) members.The proposed model is able to predict the non linear relation between the applied tensile load and the fibre displacement and is particularly suitable for synthetic fibres that may exhibit large axial elongation and sliphardening interface behavior. Indeed, the balance conditions between the axial load and the shear stress arising on the fibre surface in frictional contact with the matrix are imposed on the deformed configuration. The frictional bond strength is assumed to increase with slippage distance as a consequence of the increasing abrasion of the fibre surface occurring for polymeric fibres that have been subjected to surface treatments. The model is also suitable for metallic fibres if constant friction or slipsoftening interface behavior is assumed instead. The results provided by the proposed model are compared with the results obtained from pullout tests performed on polymeric fibres embedded in a cement matrix, both for treated and untreated fibres. After conveniently setting the constitutive parameters, the model proves to be able to predict the experimental curves accurately.
2015
 AniCryDe: calculation of elastic properties in silicon and germanium crystals
[Articolo su rivista]
Camattari, R.; Lanzoni, L.; Bellucci, V.; Guidi, V.
abstract
A code to calculate the anisotropic elastic properties in a silicon or germanium
crystal is introduced. The program, namedAniCryDe, allows the user to select
the crystallographic configuration of interest. For the selected crystallographic
orientation,AniCryDecalculates several key mechanical parameters, such as
Young’s modulus, Poisson’s ratio and the shear modulus. Furthermore, the
program displays both the compliance and the stiffness tensors concerning the
crystallographic orientation of interest. The code enables the user to set several
parameters through a userfriendly control stage. As a result, the user obtains
the complete displacement field of a deformed crystal and the curvature of any
crystallographic plane. Manufacturing wafer defects such as miscut and misflat
angle are also taken into account.
2015
 Axisymmetric loading of an elasticplastic plate on a general twoparameter foundation
[Articolo su rivista]
Lanzoni, Luca; Nobili, Andrea; Radi, Enrico; Sorzia, Andrea
abstract
The load carrying capacity and collapse scenarios for an infinite elasticplastic plate resting on a twoparameter
elastic foundation uniformly loaded on a small circular footprint are investigated in a general
framework of stiffness and yield parameters. The present work extends the study already presented for
a specific value of the Pasternak modulus and it allows the investigation of the influence of the stiffness
property of the underlying soil and the amplitude of the loaded region on the load carrying capacity
of the plate and the corresponding collapse mechanism. Moreover, the present analysis allows for the evaluation of the transverse deflection, slope, radial and circumferential bending moments, shearing force within the plate and the reactive pressure of the elastic subgrade at the onset of the plastic collapse together with their dependence on the foundation moduli. The effect of the ratio between negative and positive yield moments is also investigated. The amplitude and assembly of plastic regions at the onset of the plastic collapse are discussed in some detail.
2015
 Elasticplastic plates on a nonlocal subgrade
[Abstract in Atti di Convegno]
Sorzia, Andrea; Lanzoni, Luca; Nobili, Andrea; Radi, Enrico
abstract
A thin elasticplastic Kirchhoff plate resting on a nonlocal foundation subjected to an axisymmetric load distribution is investigated in the present work. The plate is assumed to obey to the Johansen yield criterion with associative flow rule, whereas the subgrade is modeled like an elastic nonlocal twoparameter foundation. The analysis of an elasticplastic plate resting on a Winkler soil has been developed previously. Later, a generalization has been proposed by introducing a two parameter foundation, but only for a specific ratio between the soil parameters. The present study extends the previous analysis by considering an arbitrary Pasternak soil.
A method based on a contour integral is adopted here to solve in closed form the fourthorder linear ODE governing the elasticplastic region of the plate. The boundary conditions are set by imposing proper continuity conditions for displacement, rotation, bending moment and shear force across the boundaries between the annular regions of the plate. Two different mechanisms at the onset of collapse are found, depending mainly on the amplitude of the loaded region as well as on the stiffness of the plate. The study allows to investigate the effect induced by the Pasternak soil parameters on the ultimate bearing capacity of the plate and the corresponding collapse mechanism. In particular, it is found that a circular elasticplastic region with positive yield lines in both radial and circumferential directions occurs under the loaded area of the plate, whereas such a region degenerates into a point size plastic hinge for a Winkler foundation. Moreover, the amplitude of the loaded region is found to significantly affect the response of the system, particularly in terms of the reactive pressure distribution arising in the underlying foundation.
The study covers a wide array of practical applications in structural and civil engineering, ranging from the assessment of the ultimate bearing capacity of fiber reinforced industrial floors to the behavior of rigid road pavements near its limit state and the ultimate conditions of a building foundation.
2015
 Equilibrium configurations and stability of a damaged body under uniaxial tractions.
[Articolo su rivista]
Lanzoni, Luca; Tarantino, Angelo Marcello
abstract
This paper deals with the equilibrium problem in nonlinear dissipative inelasticity of damaged bodies subject to uniaxial loading.
2015
 FRC plates on nonlocal subgrade
[Relazione in Atti di Convegno]
Lanzoni, Luca; Nobili, Andrea; Radi, Enrico; Sorzia, Andrea
abstract
The present work deals with the mechanical behavior of a large FRC slab bilaterally supported by a nonlocal elastic soil. The slab is modelled as a ductile Kirchhoff plate laying on a twoparameter elastic foundation and transversally loaded by a uniform pressure applied on a circular area, thus making the problem axisymmetric. This layout covers a wide array of practical applications in the framework of structural and civil engineering, ranging from the assessment of the ultimate bearing capacity of industrial floors, road pavements and building raft foundation. The analysis allows to evaluate the effects induced by the nonlocal character of the foundation on the ultimate carrying capacity and collapse mechanism of FRC slabs.
2015
 Ion implantation for manufacturing bent and periodically bent crystals
[Articolo su rivista]
Bellucci, Valerio; Camattari, Riccardo; Guidi, Vincenzo; Mazzolari, Andrea; Paternã², Gianfranco; Mattei, Giovanni; Scian, Carlo; Lanzoni, Luca
abstract
Ion implantation is proposed to produce selfstanding bent monocrystals. A Si sample 0.2mm thick was bent to a radius of curvature of 10.5m. The sample curvature was characterized by interferometric measurements; the crystalline quality of the bulk was tested by Xray diffraction in transmission geometry through synchrotron light at ESRF (Grenoble, France). Dislocations induced by ion implantation affect only a very superficial layer of the sample, namely, the damaged region is confined in a layer 1Î¼m thick. Finally, an elective application of a deformed crystal through ion implantation is here proposed, i.e., the realization of a crystalline undulator to produce Xray beams.
2015
 On the problem of a Timoshenko beam bonded to an elastic halfplane
[Abstract in Atti di Convegno]
Lanzoni, Luca; Radi, Enrico; Sorzia, Andrea
abstract
The contact problem of beams, rods, ribs and plates bonded to a halfplane has been widely investigated by many Authors. In particular, the problem of prismatic beams resting on a finite or semiinfinite elastic substrate deserves great interest because its practical applications in many engineering application. As an example, Shield and Kim (1992) investigated the problem of an EuleroBernoulli beam resting on an elastic halfplane under symmetric loading conditions, founding the interfacial stresses as well as the SIFs at the edges of the beam. The Authors also studied the effect induced by an elasticperfectly plastic cohesive interface. Nonetheless, a complete analytical study of the contact problem of a Timoshenko beam bonded to a halfplane cannot be found in literature.
The present study concerns the contact problem of a Timoshenko beam resting on an elastic halfplane under general edge loading. The problem is solved by imposing the strain compatibility condition between the beam and the halfplane leading to a. system of 2 integral equations, which is transformed to an algebraic system equations by using series expansions in Jacobi polynomials for the displacement field and Chebyshev polynomials for shear and peeling stresses along the interface.
2015
 Partially coated ceramic layer under thermal stress
[Relazione in Atti di Convegno]
Falope, FEDERICO OYEDEJI; Lanzoni, Luca; Radi, Enrico
abstract
Thin films and coatings technology has known a large development in the last decades due to the large number of devices involving thin films employed in hightech industries, mainly in microelectronics, electrochemistry, semiconductors and optical electronics. Indeed, realization of MEMS and NEMS used into biomedical components, chemical reactors, integrated circuit, solar cells, flat panels displays, sensors, insulator and protection systems, transducers, highprecision measuring instruments, etc. are examples of important applications having significant commercial implication. Recently, many theoretical and experimental studies have been focused on the feasibility of a crystalline undulator (CU), that is a special kind of MEMS realized by covering a ceramic substrate. This microdevice can be used to produce a coherent beam of Xray at high energy levels by exploiting the channelling phenomenon [1]. The substrate generally consists of a Silicon or Germanium crystalline plate covered by a thin film deposed on both surfaces by a proper chemical process (e.g. LPCVD) at high temperature. Through a suitable photolithographic process, the film is properly patterned in order to impart a periodic deformation to the crystalline substrate, suitable to produce coherent interaction with a beam particles. The system adopts a periodic curvature as a result of the misfit strain due to the different thermal expansivities of the layer and the film
The present work provides an extension of the paper [2] by taking into account the anisotropy of the substrate and coatings. The substrate is modelled as a 2D orthotropic elastic layer under plane strain conditions, whereas the film is assumed to behave like a membrane, thus neglecting its flexural stiffness. The problem is formulated by imposing perfect adhesion between the film and the substrate, thus leading to a singular integral equation. The problem can be reduced to a linear algebraic system by using a series expansion of Chebyshev polynomials for the interfacial shear stress and Fourier series expansion for the displacement field. The effects of anisotropy of the materials are then examined and discussed.
2014
 A cracked infinite Kirchhoff plate supported by a twoparameter elastic foundation
[Articolo su rivista]
Nobili, Andrea; Radi, Enrico; Lanzoni, Luca
abstract
This paper presents a fullfield solution for the linear elastostatic problem of a homogeneous infinite Kirchhoff plate with a semiinfinite line crack resting on a twoparameter elastic foundation. The same model describes the problem of a cracked plate equibiaxially loaded in its midplane by a constant normal force and, as a limiting case, the problem
of a cracked spherical shell. The fullfield solution is obtained in closed form through the WienerHopf method in terms of Fourier integrals. The stressintensity factor (SIF) for the case of symmetric and skewsymmetric loading conditions are obtained and the role of the soil parameters discussed. In particular, it is shown that a purely local model (Winkler) is unable to provide a safeproof design limit.
2014
 Damaged hyperlastic membranes
[Articolo su rivista]
Lanzoni, Luca; Tarantino, Angelo Marcello
abstract
This paper deals with equilibrium problems in nonlinear dissipative
inelasticity of damaged membranes. The inelastic constitutive law
is obtained by modifying the classical constitutive law for a hyperelastic
isotropic material through a proper damage function, which allows
to measure the effective stress and the dissipated energy. After making
the constitutive modeling, the boundaryvalue problem is formulated
for a damaged membrane subjected to biaxial loadings. The purpose
of the analysis is to understand how behaves a membrane that, during
the deformation process, experiences a progressively increasing damage.
Equilibrium multiple branches of symmetric and asymmetric solutions,
together to bifurcation points, are computed and it is shown how damage
can alter these equilibrium paths with respect to the virgin undamaged
case. In particular, the stress reductions caused by damage can give
rise to transitions of the constitutive behavior from hardening type
to the softening one. These changes can considerably affect the quality
of the equilibrium solutions. Accordingly, the analysis is completed
by assessing the stability of the solutions. For this aim, the stability
analysis based on the energetic criterion is extended to damaged membranes.
2014
 Experimental evidence of planar channeling in a periodically bent crystal
[Articolo su rivista]
E., Bagli; L., Bandiera; V., Bellucci; A., Berra; R., Camattari; D., De Salvador; G., Germogli; V., Guidi; Lanzoni, L; D., Lietti; A., Mazzolari; M., Prest; V. V., Tikhomirov; E., Vallazza
abstract
The usage of a crystalline undulator (CU) has been identified as a promising solution for generating powerful and monochromatic γ rays. A CU was fabricated at Sensors and Semiconductors Lab (SSL) through the grooving method, i.e., by the manufacturing of a series of periodical grooves on the major surfaces of a crystal. The CU was extensively characterized both morphologically via optical interferometry at SSL and structurally via Xray diffraction at ESRF. Then, it was finally tested for channeling with a 400 GeV/c proton beam at CERN. The experimental results were compared to Monte Carlo simulations. Evidence of planar channeling in the CU was firmly observed. Finally, the emission spectrum of the positron beam interacting with the CU was simulated for possible usage in currently existing facilities.
2014
 Full field solution for a rectilinear crack in an infinite Kirchhoff plate supported by a Pasternak elastic foundation.
[Abstract in Atti di Convegno]
Nobili, Andrea; Radi, Enrico; Lanzoni, Luca
abstract
The failure of cracked ceramic components is governed by the stresses in the neighbouring of the crack tip, which is described by the stress intensity factor (SIF).
Despite the availability of several handbooks for SIFs, very few fullfield solutions are available for cracked plates resting on an elastic foundation. This lack of results is problematic, since this situation often occur in practice (e.g. roadways, pavements, floorings, etc.).
Furthermore, when some results are available, they never involve the foundation's mechanical properties alone.
For instance, the problem of a finite crack in an infinite Kirchhoff plate supported by a Winkler foundation is considered in [1] and it is reduced to a singular integral equation. However, since two length scales exist in the problem (the crack length and the foundation relative Winkler modulus), the SIF may be related to some dimensionless ratio of them and not directly to the foundation's mechanical property. In actual facts, this outcome stems from the Winkler approximation to the foundation and not from the physical feature of the problem. The fullfield solution for a semiinfinite rectilinear crack in an infinite Kirchhoff plate resting on a Winkler foundation is found in [2]. Since this is a selfsimilar problem, no characteristic length scale exists. Application of the above results to road and airport pavements is given in [3]. As a result, the influence of the pavement foundation on the SIF cannot be properly assessed.
Several papers address crack problems in plate theory and a literature review of the stress field at the crack tip in thin plates and shells is given in [4] along with comparison with the available experimental results.
The present work deals with the elastostatic problem of a semiinfinite rectilinear crack in an infinite Kirchhoff plate resting on a twoparameter elastic foundation under very general loading conditions. The foundation, also termed Pasternaktype, is weakly nonlocal, as it accommodates for coupling among the independent springs of a purely local model (i.e. the Winkler model).
The same model governs the problem of a Kirchhoff plate equibiaxially loaded in its midplane. The Pasternak foundation accounts for two length scales such that the whole problem is governed by a parameter η expressing the soil to plate relative stiffness. The discussion was addressed in a previous paper [5] but therein limited to the range 0 < η < 1, where the limiting case as η → 0 recovers the nonlocal Winkler model. In the present work the analysis has been extended to the full range of values for the paremeter η. The problem is formulated in terms of a pair of dual integral equations solved through the Wiener–Hopf technique. Numerical results are given for the full field bending and shear stress field within the plate, the corresponding SIFs are obtained and some conclusions drawn.
2014
 On the stability loss for an euler beam resting on a tensionless pasternak foundation
[Articolo su rivista]
Nobili, Andrea; Lanzoni, Luca
abstract
In the present work, the tensionless contact problem of an Euler–Bernoulli beam of finite length resting on a twoparameter Pasternaktype foundation is investigated. Owing to the tensionless character of the contact, the beam may liftoff the foundation and the point where contact ceases and detachment begins, named contact locus, needs be assessed. In this situation, a onedimensional free boundary problem is dealt with. An extra condition, in the form of a homogeneous secondorder equation in the displacement and its derivatives, is demanded to set the contact locus and it gives the problem its nonlinear feature. Conversely, the loading and the beam length may be such that the beam rests entirely supported on the foundation, which situation is governed by a classical linear boundary value problem. In this work, contact evolution is discussed for a continuously varying loading condition, starting from a symmetric layout and at a given beam length, until overturning is eventually reached. In particular, stability is numerically assessed through the energy criterion, which is shown to stand for the free boundary situation as well. At overturning, a descending pathway in the system energy appears and stability loss is confirmed.
2014
 Strato in misto cementato per pavimentazioni stradali
[Brevetto]
Tarantino, Angelo Marcello; Nobili, Andrea; Grilli, Andrea; Lanzoni, Luca
abstract
Impiego di materiali fibrati per la realizzazione dei sottofondi stradali, allo scopo di ridurre la manutenzione.
2014
 Ultimate carrying capacity of elasticplastic plates on Pasternak foundation.
[Articolo su rivista]
Lanzoni, Luca; Radi, Enrico; Nobili, Andrea
abstract
In the present work, the problem of an infinite elasticperfectly plastic plate under axisymmetrical loading conditions resting on a Pasternak elastic foundation is considered. The plate is assumed thin, thus making possible to neglect the shear deformation according to the classical Kirchhoff theory. Yielding is governed by the Johansen’s yield criterion with associative flow rule. An uniformly distributed load is applied on a circular area on the top of the plate. As the load is increased, a circular elasticplastic region spreads out starting from the center of the loaded area, whereas the outer unbounded region behaves elastically. Depending on the size of the loaded area, under the collapse load the inner elasticplastic region can be separated into two or three different regions, corresponding to different yield loci. A closed form solution of the governing equations for each region is found for a special value of the ratio between Pasternak soil moduli. The performed analysis allows to estimate the elasticplastic behavior of the plate up to the onset of collapse, thus providing the collapse load of the plate, the corresponding plastic mechanism and the size of the elasticplastic regions. The influence of the soil moduli, plate bending stiffness, and size of the loaded area on the ultimate bearing capacity of the plate is then investigated in detail.
2013
 Experimental analysis and modeling of selfstanding curved crystals for focusing of Xrays
[Articolo su rivista]
Camattari, Riccardo; Guidi, Vincenzo; Lanzoni, Luca; Neri, Ilaria
abstract
Novel applications can be attained through
the usage of bent crystals as optical components for
the challenge of focusing hard X andγrays by Bragg
diffraction. Nuclear astrophysics, nuclear medicine
and homeland security would highly benefit from
such optics, because they all share the same need for
efficient X and γray focusing systems. With this
aim, selfstanding bent silicon crystals have been reproducibly attained thanks to the method of surface
grooving. An extensive study has been worked out to
understand the process of substrate deformation. By
adjusting experimental parameters, very good control
of the curvature is afforded. Process of deformation
has been modeled in terms of irreversible compression
occurring in the material close to the grooves. The underlying silicon was treated as an anisotropic medium
elastically reacting to the state of stress provided by
the grooves. Comparison between experimental results and theoretical expectations was satisfactorily
achieved.
2013
 Experimental investigation and monitoring of a polypropylenebased fiber reinforced concrete road pavement
[Articolo su rivista]
Nobili, Andrea; Lanzoni, L.; Tarantino, Angelo Marcello
abstract
In this work, basic guidelines are provided for the design of a polypropylenebased fiber reinforced (PFRC) road pavement.
2013
 The bending stress in a cracked Kirchhoff plate resting on a Pasternak foundation
[Relazione in Atti di Convegno]
Lanzoni, Luca; Nobili, Andrea; Radi, Enrico
abstract
The problem of a rectilinear semiillimitate crack in a Kirchhoff elastic plate laying on a weakly nonlocal elastic twoparameter (Pasternak) foundation and subject to transversal loadings applied on the plate surfaces is studied in the present work. By extending the approach developed
by Ang et al. [1] for a plate on a Winkler elastic foundation, the analytical fullfield solution is obtained by solving a system of dual integral equations. In particular, the kernel function is factorized by using a procedure based on the Cauchy theorem, similar to the WienerHopf method
used in the solution of antiplane fracture problems [2, 3].
Closedform solutions are thus provided for displacement, bending moment and shear force per unit length along the crack line. The ratioes between the subgrade parameters and flexural rigidity of the plate allow introducing two
characteristic lengths, whose influence on the bending stress intensity factor and fracture toughness of the plate is then investigated.
The governing equation is closely related to the bending problem of initially curved thin sheets under transversal loading and subjected to a constant normal stress, so that results apply to such situation as well. Accordingly, this is one of the few closedform solutions available for initially
curved cracked thin sheets.
2013
 The bending stress in a cracked ceramic plate resting on a two parameter elastic grade
[Abstract in Atti di Convegno]
Lanzoni, Luca; Nobili, Andrea; Radi, Enrico
abstract
The problem of a rectilinear semiillimitate crack in a ceramic plate laying on a weakly nonlocal elastic twoparameter (Pasternak) foundation and subject to transversal loadings applied on the plate surfaces is studied in the present work.
The analytical fullfield solution is obtained by solving a system of dual integral equations. In particular, the kernel function is factorized by using a procedure based on the Cauchy theorem, similar to the WienerHopf method used in the solution of antiplane fracture problems.
Closedform solutions are thus provided for displacement, bending moment and shear force per unit length along the crack line.
The ratioes between the subgrade parameters and flexural rigidity of the plate allow introducing two characteristic lengths, whose influence on the bending stress intensity factor and fracture toughness of the plate is then investigated.
2012
 Interfacial shear stress analysis of bar and thin film bonded to 2D elastic substrate using a coupled FEBIE method
[Articolo su rivista]
Tullini, Nerio; Tralli, Antonio; Lanzoni, Luca
abstract
In the present work, a Finite ElementBoundary Integral Equation (FEBIE) coupling method is proposed to investigate the problem of axially loaded thin structures bonded to a homogeneous elastic halfplane. Making use of a mixed variational formulation including the Green function of the substrate, the axial displacement of the bar is interpolated using Lagrange polynomials of first or second order, whereas the interfacial shear stress is approximated by piecewise constant functions. Bars subject to different load conditions are investigated, including the case of a bar partially detached from the substrate. The strength of interfacial stress singularities is investigated in detail. Â© 2012 Elsevier B.V. All rights reserved.
2012
 MISSION PROFILE FOR AGRICULTURAL TRACTORS: A FOCUS ON HYDRAULIC CIRCUIT
[Relazione in Atti di Convegno]
Borghi, Massimo; Zardin, Barbara; Belluzzi, Francesco; Lanzoni, Luca
abstract
Mission profile for agricultural vehicles aims to define a picture of a typical working condition of the vehicle. The collection of these pictures gives information about the performance, the efficiency, and the eventual critical conditions with reference to the kind of operation and terrain. Unfortunately, to be at the same time quick, easy to be interpreted and effective, this analysis has to neglect the details and to take into consideration the whole situation. However, detailed considerations about the efficiency of the vehicle subsystems and of their components may derive only from a deeper analysis and it is from these information that designers and technicians can derive improvements of the system.
A promising way to solve this discrepancy is to integrate experimental analysis with simulation: from experimental test on field is possible to define several duty cycles representing different working conditions on the vehicle. These data can then be used as input in a simulation model representing the system, able to replicate its dynamic behaviour. Finally, possible modifications of the system architecture or components, aimed at the improvement of the performance or efficiency, may be more easily tested on the virtual model. In this paper this methodology is presented with reference to the hydraulic circuit of an agricultural tractor, in particular the portion related to the managing of the auxiliary utilities, showing the capability to represent in detail the behaviour of the system and to explore the critical performances.
2012
 Performance evaluation of a polypropylenebased drawwired fibre for concrete structures
[Articolo su rivista]
Lanzoni, Luca; Nobili, Andrea; Tarantino, Angelo Marcello
abstract
Abstract. A polypropylenebased drawwired fibre suitable for fibre reinforced concrete (FRC) is studied and its effect on flexural behaviour, toughness and shrinkage cracking is shown. In order to assess the perfor mance offered by such a fibre over commercially available synthetic and metallic ones, comparative tests are carried out with respect to standard fourpoint bending and constrained shrinkage behaviour. The experimental evidence shows that FRC reinforced with these fibres possesses interesting structural fea tures; in particular, fibres significantly improve crack resistance while enhancing toughness and durabil ity of FRC elements. Equally important, such behaviour is gained without significantly affecting the workability of the mixture.
2011
 Analysis of stress singularities in thin coatings bonded to a semiinfinite elastic substrate
[Articolo su rivista]
Lanzoni, Luca
abstract
The interfacial stress arising between thin structures bonded to a 2D elastic substrate has been investigated in the present work. Chebyshev polynomials have been adopted to approximate the shear stress
occurring across the contact region. Perfect adhesion has been assumed among the coating structures
and the underlying substrate, leading to a singular integral equation which has been reduced to an algebraic system. Thin bonded structures having several geometric configurations under different load conditions have been considered. In particular, the stress concentration in the neighborhood of the coating edges and around the points of load application has been evaluated in detail.
2011
 Hazard Evaluation in Valparaíso: The MAR VASTO Project
[Articolo su rivista]
Indirli, M.; Razafindrakoto, H.; Romanelli, F.; Puglisi, C.; Lanzoni, L.; Milani, E.; Munari, M.; Apablaza, S.
abstract
The Project "MAR VASTO" (Risk Management in Valparaíso/Manejo de Riesgos en Valparaíso), funded by BID/IADB (Banco InterAmericano de Desarrollo/InterAmerican Development Bank), has been managed by ENEA, with an Italian/Chilean joined partnership and the support of local institutions. Valparaíso tells the neverending story of a tight interaction between society and environment and the city has been declared a Patrimony of Humanity by UNESCO since 2003. The main goals of the project have been to evaluate in the Valparaíso urban area the impact of main hazards (earthquake, tsunami, fire, and landslide), defining scenarios and maps on a georeferenced GIS database. In particular, for earthquake hazard assessment the realistic modelling of ground motion is a very important base of knowledge for the preparation of groundshaking scenarios which serve as a valid and economic tool to be fruitfully used by civil engineers, supplying a particularly powerful tool for the prevention aspects of Civil Defense. When numerical modelling is successfully compared with records (as in the case of the Valparaíso, 1985 earthquake), the resulting synthetic seismograms permit the generation of groundshaking maps, based upon a set of possible scenario earthquakes. Where no recordings are available for the scenario event, synthetic signals can be used to estimate ground motion without having to wait for a strong earthquake to occur (predisaster microzonation). For the tsunami hazard, the available reports, [e. g., SHOA (1999) Carta de Inundacion por Tsunami para la bahia de Valparaíso, Chile, http://www. shoa. cl/servicios/citsu/citsu. php], have been used as the reference documents for the hazard assessment for the Valparaíso site. The deep and detailed studies already carried out by SHOA have been complemented with (a) sets of parametric studies of the tsunamigenic potential of the 1985 and 1906 scenario earthquakes; and (b) analytical modelling of tsunami waveforms for different scenarios, in order to provide a complementary dataset to be used for the tsunami hazard assessment at Valparaíso. In addition, other targeted activities have been carried out, such as architectonic/urban planning studies/vulnerability evaluation for a pilot building stock in a historic area and a vulnerability analysis for three monumental churches. In this paper, a general description of the work is given, taking into account the in situ work that drove the suggestion of guidelines for mitigation actions. © 2010 Springer Basel AG.
2011
 On the contact problem of beams resting on tensionless twoparameter foundations
[Abstract in Atti di Convegno]
Nobili, Andrea; Lanzoni, Luca
abstract
In the present work, the tensionless contact problem of an EulerBernoulli beam of finite length resting on a twoparameter foundation is investigated, with special regard to the Reissner soil model. Owing to the tensionless nature of the contact, the beam may liftoff the foundation and the condition setting the point where contact ceases and detachment begins, named contact locus, needs to be assessed. Such condition is in the form of a homogeneous secondorder form in the displacement and its derivatives, which gives the problem a nonlinear feature. Moreover, the loading and the beam length may be such that the beam rests entirely supported on the foundation, which situation is governed by a different set of boundary conditions (BCs).Through a variational approach, the proper set of BCs at the contact loci have been determined elsewhere and some numerical examples given, with special regard to the Pasternak foundation. In this work, the BCs are put to advantage to discuss a number of relevant situations concerning beams on a Reissner foundation. Indeed, the Reissner simplified continuum (RSC) model is often regarded, for instance in the realm of soilstructure interaction, as the most effective soil model which retains a certain degree of simplicity. Symmetric as well as nonsymmetric contact scenarios are considered and the elastic energy of the system is plotted onto the equilibrium candidates, showing that the alleged solutions are indeed energy stationary points. The problem of finding the limiting loading at equilibrium, on the verge of complete detachment, is also touched upon.
2011
 Patterning and modeling of mechanically bent silicon plates deformed through coactive stresses
[Articolo su rivista]
Guidi, V.; Lanzoni, L.; Mazzolari, A.
abstract
In the present work a technique to impart a controlled deformation to a substrate through deposition of a thin film is shown. Such a technique allows filmsubstrate systems to be tailored with a desired shape for various applications. An analytical model has been applied to calculate the displacements and stresses of a patterned crystalline substrate. Analytical results have also been validated via Finite Element simulations. Si substrates have been patterned with Si3N4 and measurements of the transverse displacement were found to agree with the theoretical predictions. Â© 2011 Elsevier B.V. All rights reserved.
2010
 Electromechanical instability in layered materials
[Articolo su rivista]
Nobili, Andrea; Lanzoni, Luca
abstract
This paper deals with instability of a semiinfinite strip of polarizable layered material which is subjected to both a boundary displacement and an externally applied electrostatic potential in a plane deformation setting. Since the material is polarizable, it contributes (here in a linear fashion) to the applied electrostatic field. The nonlinear equilibrium problem is solved through a perturbative scheme and the Euler–Lagrange equations are presented. Closedform solutions are found for some special situations and they are checked against some established results. It is shown that the general condition which lends the instability threshold is obtained enforcing that a third degree polynomial admits a double negative real solution. This amounts to seeking the roots of the discriminant of the polynomial and to checking two conditions. The negative double root yields the perturbation frequency. In the general case, a numerical solution is called upon and an instability curve, in terms of electrostatic potential vs. boundary displacement at threshold, is found. At reaching such curve, the material suddenly superposes to a homogeneously stretched configuration a periodic undulation in both the displacement and the electrostatic fields. A parametric analysis is put forward and an interesting nonmonotonic behavior is found. The frequency as well as the amplitude of both the mechanical and the electrostatic undulations are found and discussed.
2010
 Study of anticlastic deformation in a silicon crystal for channeling experiments
[Articolo su rivista]
Guidi, V.; Lanzoni, L.; Mazzolari, A.
abstract
Anticlastic deformationADis an established mechanical property of isotropic solid bodies, which
has been recently used to steer particle beams through channeling in Si crystals. An analysis of AD
in an anisotropic material, such as Si, has been worked out with particular emphasis to the cases
used in channeling experiments. Both a theoretical model and finite element simulations were
developed and compared to experimental data achieved by optical profilometry on bent Si crystals.
A quantifier of the extent of AD, namely the ratio between primary and secondary curvature radii,
has been found to be orientation dependent and determined analytically. The realistic case of crystal
bending by a mechanical holder has been studied for applications. We addressed the case of the
holder with a crystal at the energy currently under operation in the CERN super proton synchrotron
and its possible extension to higher energy cases such as for the large hadron collider.
Anisotropydriven torsion of the crystal was investigated, determining a limitation to the portion of
the crystal suitable for channeling. The geometry of the jaws clamping the crystal was considered
too
2009
 Thermally induced deformations in a partially coated elastic layer
[Articolo su rivista]
Lanzoni, L.; Radi, Enrico
abstract
The problem of a thin film coated on an elastic layer and subject to a thermal variation is analytically investigated in the present work. The analysis is developed in order to assess the mechanical behaviour of a crystalline undulator designed for obtaining high emission radiations through channelling phenomenon.It consists in a plane silicon wafer alternately patterned with thin films in silicon nitride on both surfaces. The system adopts a periodic curvature as a result of the misfit strain due to the different thermal expansivities of the layer and the film. The problem is governed by an integral equation which can be reduced to a linear algebraic system by approximating the unknown interfacial shear stress via series expansion of Chebyshev polynomials.
2008
 On the mechanical behaviour of a crystalline undulator
[Articolo su rivista]
Lanzoni, L.; Mazzolari, A.; Guidi, V.; Tralli, A.; Martinelli, G.
abstract
A crystalline undulator is a newly proposed compact device to generate coherent electromagnetic waves. The crystalline undulator is a microelectromechanical system that relies on silicon microfabrication. In the present work, the mechanical behaviour of a crystalline undulator with submillimetric period obtained by patterning the surfaces of a silicon lamina with alternate strips has been investigated. The anisotropy of the silicon substrate and the geometrically nonlinear behaviour of the device have been discussed. Sensitivity study has been performed for defining the optimal thickness and width of the strips. Finally, an analytical model is proposed to evaluate the displacements and local effects such as interfacial shear stress concentrations. Â© 2008 Elsevier Ltd. All rights reserved.
2007
 Design of a crystalline undulator based on patterning by tensile Si3N4Si3N4 strips on a Si crystal
[Articolo su rivista]
Guidi, V.; Lanzoni, L.; Mazzolari, A.; Martinelli, G.; Tralli, A.
abstract
A crystalline undulator consists of a crystal with a periodic deformation in which channeled particles
undergo oscillations and emit coherent undulator radiation. Patterning by an alternate series of
tensile Si3N4 strips on a Si crystal is shown to be a tractable method to construct a crystalline
undulator. The method allows periodic deformation of the crystal with the parameters suitable for
implementation of a crystalline undulator. The resulting periodic deformation is present in the bulk
of the Si crystal with an essentially uniform amplitude, making the entire volume of the crystal
available for channeling and in turn for emission of undulator radiation. ©2007 American Institute
of Physics.
2007
 On the problem of a coated elastic layer subjected to residual thermal stress
[Relazione in Atti di Convegno]
Lanzoni, L.; Radi, Enrico
abstract
In the present work the problem of thin surface coatings of an elastic layer subject to a residual thermal stress is analytically investigated. The system adopts a curvature as a result of the misfit strain due to the different thermal expansivities of the layer and coatings. The problem is governed by a singular integral equation which can be reduced to a linear algebraic system by approximating the unknown interfacial shear stress via series expansion of Chebyshev polynomials. The present analysis is developed in order to assess the mechanical behaviour of a crystalline undulator designed for obtaining high emission radiations through channelling phenomenon.
2007
 On the seismic response of a flexible wall retaining a viscous poroelastic soil
[Articolo su rivista]
Lanzoni, L.; Radi, Enrico; Tralli, A.
abstract
A simple and reliable method is presented for the seismic analysis of a flexible wall retaining a layer of fluidsaturated viscous and poroelastic soil. A viscous version of the linear poroelastic Biot model is adopted for the description of the soil dissipative behavior. The effects of the wall flexibility and the mechanical properties of the soil on the amplitude and distribution of the pressures and the associated forces acting on the wall under harmonic loadings are firstly analyzed. The pseudostatic response is then recovered as a particular case for a vanishing small frequency of excitation. Finally, the response of the soil–wall system to generic seismic excitation is obtained using the Discrete Fourier Transform (FFT) method through the superposition of the contribution of each harmonic component of the ground acceleration spectrum. The analysis of the dynamic response obtained for different geometries of the wall and mechanical soil behavior allowed the relative importance of the various parameters involved in the seismic response of the system to be assessed.
2007
 Ricoprimento sottile periodico di un mezzo elastico soggetto a stress termico residuo
[Abstract in Atti di Convegno]
Lanzoni, Luca; Radi, Enrico
abstract
Nel presente lavoro viene studiato il problema di contatto e adesione tra uno strato di silicio parzialmente ricoperto da un film sottile di nitruro di silicio, soggetto ad uno stress termico residuo. Questo tipo di microstruttura trova rilevanti applicazioni nel processo di channeling di fasci di particelle ad alta energia. In particolare, si considera un modello periodico con film disposti ad intervalli regolari sia sulla superficie di un semispazio elastico che di uno strato di spessore finito. Utilizzando il metodo delle trasformate integrali, il problema si può formulare attraverso un sistema di equazioni integrali duali. Tale sistema può quindi ricondursi ad un'unica equazione integrale di Fredholm, che può risolversi attraverso tecniche di approssimazione basate sull'impiego dei polinomi di Chebyshev.
2006
 Modelli analitici per lo studio della risposta dinamica di paratie flessibili soggette ad azioni sismiche
[Articolo su rivista]
Lanzoni, L.; Fioravante, V.; Radi, Enrico; Tralli, A.
abstract
Nel lavoro vengono presentati due modelli analitici sviluppati per descrivere la complessa interazione dinamica fra il terreno ed una paratia incastrata alla base. Per superare i limiti dei modelli pseudoelastici suggeriti dagli Eurocodici, i modelli sviluppati consentono di valutare il contenuto in frequenza del sisma di progetto, la rigidezza della paratia e le proprietà elastiche e reologiche del terreno. Si rende inoltre possibile simulare il comportamento dinamico dell'insieme terrenoopera di sostegno in presenza di una forzante comunque variabile nel tempo, applicando la trasformata discreta di Fourier. La risposta dinamica relativa all'interazione con terreni poco permeabili viene simulata con un modello costitutivo viscoelastico, mentre per terreni aventi granulometria maggiore si adotta un modello poroviscoelastico. La risposta dei modelli ad alcuni accelerogrammi reali viene quindi comparata con i risultati riportati nella letteratura tecnica.
2005
 On the dynamic response of flexible walls retaining a dissipative, dried or fluidsaturated porous media
[Relazione in Atti di Convegno]
Lanzoni, L; Radi, Enrico; Tralli, A.
abstract
In the present work the problem of thin surface coatings of an elastic layer subject to a residual thermal stress is analytically investigated. The system adopts a curvature as a result of the misfit strain due to the different thermal expansivities of the layer and coatings. The problem is governed by a singular integral equation which can be reduced to a linear algebraic system by approximating the unknown interfacial shear stress via series expansion of Chebyshev polynomials. The present analysis is developed in order to assess the mechanical behaviour of a crystalline undulator designed for obtaining high emission radiations through channelling phenomenon
2005
 Sulla risposta dinamica di paratie flessibili incastrate soggette a sollecitazioni sismiche in depositi alluvionali
[Articolo su rivista]
Lanzoni, L.; Fioravante, V.; Radi, Enrico; Tralli, A.
abstract
Nel lavoro sono illustrati alcuni risultati di una ricerca volta a valutare la complessa risposta dinamica di una paratia flessibile incastrata, mediante due modelli lineari, uno viscoelastico, applicabile a terreni poco permeabili, ed uno poroviscoelastico,per terreni a granulometria maggiore.A differenza dei modelli pseudostatici suggeriti dagli Eurocodici, i modelli sviluppati forniscono una anlaisi dinamica completa, in quanto consentono di valutare il contenuto energetico del sisma di progetto, e la reale rigidezza rigidezza della paratia. Al fine di valutare l'efficacia dei modelli proposti e per quantificare le differenze delle sollecitazioni ottenute rispetto al metodo esemplificato di MononobeOkabe, sono riportati i risultati di due simulazioni finalizzate ai progetti di due opere di sostegno in due siti alluvionali interessati dal progetto dell'Idrovia Ferrarese. Le analisi sono state condotte utilizzando gli accellerogrammi registrati durante due eventi sismici recenti (Novellara (RE), 1996 e Assisi, 1997).Si rende inoltre possibile simulare il comportamento dinamico dell'insieme terrenoopera di sostegno in presenza di una forzante comunque variabile nel tempo, applicando la trasformata discreta di Fourier.