
Andrea NOBILI
Professore Associato Dipartimento di Ingegneria "Enzo Ferrari"

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 Fibre in polipropilene per calcestruzzi strutturali fibrorinforzati
[Brevetto]
Tarantino, Angelo Marcello; Nobili, Andrea
abstract
fibre sintetiche per calcestruzzi
2024
 A weakly nonlinear Love hypothesis for longitudinal waves in elastic rods
[Articolo su rivista]
Nobili, A.
abstract
When investigating nonlinear wave propagation in slender hyperelastic rods, the usual stance is to construct a reduced kinematics and then derive a system of coupled nonlinear PDEs for the unknown functions. To make further analytical progress, the linear Love hypothesis, that connects longitudinal and transversal strain, is often reverted to. The viability of this assumption, that was originally proposed within the framework of linear elasticity, remains uncertain. In this paper, a refined Love hypothesis is derived in the weakly nonlinear regime by slowtime perturbation of the motion equations. For the sake of illustration, the simplest twomodal setting is adopted. This refined Love assumption is not equivalent, not even in principle, to that derived by Porubov and Samsonov (1993) by accommodating for the free boundary conditions at the rod mantle. Besides, the perturbation process lends a unidimensional model equation which parallels that obtained by Ostrovskii and Sutin (1977) with the help of the linear Love hypothesis, with yet different coefficients in the dispersive term. The corresponding longitudinal motion is compared numerically against the solution of the bimodal nonlinear system and the transversal motion is contrasted with the linear Love hypothesis. For both motions, excellent agreement is found and the quality of the approximation extends to a wide range of values for the small parameter. Finally, within this setting, the corresponding unimodal Lagrangian is also derived, and it remains accurate regardless of the first correction terms to the linear Love hypothesis.
2024
 Analytical Description of the Bond Behavior of Thermally Preconditioned Carbon FRCM Applied onto Masonry Substrates
[Capitolo/Saggio]
Bertolli, Veronica; Signorini, Cesare; Nobili, Andrea; D'Antino, Tommaso
abstract
In the last few years, externally bonded fabricreinforced cementitious matrix (FRCM) composites have been increasingly employed as externally bonded (EB) reinforcement of existing concrete and masonry structures. Failure of EB FRCM reinforcement is generally caused by composite debonding at the matrixfiber interface. The stress transfer mechanism at the joint interface is analytically described within the fracture mechanics framework assuming a pure ModeII loading condition and a zerothickness interface, which allows for formulating the bond differential equation. Its solution requires the knowledge of the cohesive material law (CML) of the specific interface studied, often obtained by calibration of direct shear (DS) test results. In this paper, a rigidtrilinear CML is used to analytically describe the bond behavior of four control and four thermally preconditioned carbon FRCMmasonry joints subjected to singlelap direct shear test. Thermal preconditioning consists of 250minlong exposure up to 300 ℃. Stress responses obtained from the DS tests are used to calibrate the CML of the matrixfiber interface, which is then used to solve the bond differential equation. Comparison between the analytical and experimental stress responses of control and conditioned specimens sheds light on the effect of temperature exposure on the bond behavior of carbon FRCMmasonry joints.
2024
 Assessing the stresstransfer capability of mineral impregnated PBO yarns in a limestone calcined clay cementbased (LC3) matrix
[Articolo su rivista]
Signorini, C.; Nobili, A.; Liebscher, M.; Zhao, J.; Ahmed, A. H.; Koberle, T.; Mechtcherine, V.
abstract
Technical textiles made of poly(pphenylene2,6benzobisoxazole) (PBO) represent attractive candidates for strengthening and repairing damaged concrete and masonry structures, due to the outstanding durability and mechanical performance of PBO fibres. Similarly to their aramid counterparts, PBO fibres have proved very effective against dynamic and impact loading. In this contribution, the pullout behaviour of PBO multifilament yarns embedded into a blended cementbased matrix is investigated, with particular reference to its stresstransfer capacity. In addition to the asreceived PBO yarns, impregnation with a cementbased suspension, which can fully preserve the inorganic nature of the composite system, is also evaluated. Experimental results are presented and interpreted using a onedimensional mechanical model. The findings indicate that mineral impregnation of the yarns provides a 40% increase in the stresstransfer capacity with the matrix, corresponding to a halving of the anchoring length. These performance gains are also supported by a transition in the failure mechanism which shifts from frictionbased pullout to fibre rupture.
2024
 Experimental and analytical analysis of the bond alteration of impregnated carbon fibre reinforcements embedded in alkaliactivated concrete at elevated temperatures
[Articolo su rivista]
Zhao, J.; Signorini, C.; Nobili, A.; Liebscher, M.; Kohout, J.; Hajkova, P.; Mechtcherine, V.
abstract
The restricted operating temperature range of fibrereinforced polymer (FRP) systems for upgrading and retrofitting reinforced concrete structures is among the key limiting factors of this technology. Indeed, an alternative reinforcing system, known as Mineralimpregnated CarbonFibre (MCF), has recently emerged to address this issue. This paper presents an experimental investigation of the performance of MCF systems embedded in finegrained, AlkaliActivated Concrete (AAC), which have been preheated at 100 °C (or 200 °C) and then tested in pullout at the target temperature. For the purpose of assessing the bond quality against thermal exposure, results are compared with the control group (ambient temperature 20 °C), as well as with an epoxyimpregnated commercial roving. In addition, specimens are characterised at the fibretomatrix interface by microscopy and by physical–chemical analytical techniques. Experimental data are fitted onto a onedimensional stressandfriction analytical model to determine the characteristic properties of the temperaturedependent bond–slip behaviour of MCFs. Findings suggest enhanced chemical compatibility and reinforcing capabilities at elevated temperature for MCFs, primarily ascribed to the impregnation quality and to the AAC capacity to withstand thermal strain.
2024
 Hamiltonian/Stroh formalism for reversible poroelasticity (and thermoelasticity)
[Articolo su rivista]
Nobili, A.
abstract
Stroh's sextic formalism represents the equilibrium equations of anisotropic elasticity in a particularly attractive form, that is most suitable for studying interfacedominated multilayered solids, composite materials and timeharmonic problems. Taking advantage of the fact that the Stroh formalism really amounts to the canonical form of the equations in the Hamiltonian sense, the case of Biot's reversible (i.e. no fluid dissipation) poroelasticity is here addressed, in the absence of a fluid pressure gradient. This framework is the same as thermoelasticity of perfect conductors. Two Hamiltonian formulations are developed: the first describes both the solid and the fluid phases and it exhibits, besides energy conservation, momentum conservation, as a result of pressure uniformity (perfectly drained conditions). The second is restricted to the solid skeleton and perfectly parallels anisotropic elasticity, where the Stroh matrices refer to the effective stress tensor. The case of weak fluid–solid coupling is also considered and it produces a perturbation from anisotropic elasticity with the same structure as incompressibility, although in an “opposing” manner. This comparison suggests that the incompressibility limit introduced by Biot should be revised. The energy conservation integral and the edge impedance matrix are also illustrated.
2024
 Revisiting the Love hypothesis for introducing dispersion of longitudinal waves in elastic rods
[Articolo su rivista]
Nobili, A.; Saccomandi, G.
abstract
We reexamine the Love equation, which forms the first historical attempt at improving on the classical wave equation to encompass for dispersion of longitudinal waves in rods. Dispersion is introduced by accounting for lateral inertia through the Love hypothesis. Our aim is to provide a rigorous justification of the Love hypothesis, which may be generalized to other contexts. We show that the procedure by which the Love equation is traditionally derived is misleading: indeed, proper variational dealing of the Love hypothesis in a two modal kinematics (the MindlinHerrmann system) leads to the BishopLove equation instead. The latter is not asymptotically equivalent to the Love equation, which is in fact a long wave low frequency approximation of the PochhammerChree solution. However, the Love hypothesis may still be retrieved from the MindlinHerrmann system, by a slow time perturbation process. In so doing, the linear KdV equation is retrieved. Besides, consistent approximation demands that a correction term be added to the classical Love hypothesis. Surprisingly, in the case of isotropic linear elasticity, this correction term produces no effect in the correction term of the Lagrangian, so that, to first order, the same BishopLove equation is the EulerLagrange equation corresponding to a family of Love like hypotheses, all being different by the correction term. Besides, illposedness coming from nonstandard (namely non static) natural boundary conditions is now amended.
2024
 Tensile Behavior of EpoxyImpregnated Carbon FRCM Exposed to High Temperatures
[Capitolo/Saggio]
Bertolli, Veronica; Signorini, Cesare; Nobili, Andrea; D'Antino, Tommaso
abstract
Externally bonded (EB) fabricreinforced cementitious matrix (FRCM) composites, also referred to as textile reinforced concrete (TRC), are getting increasingly popular in the field of structural retrofit ting as they combine good mechanical properties with important advantages in terms of cost effectiveness, ease of intervention, and reversibility. In addition, FRCMs have good resistance to relatively elevated temperature, also by vitue of the protecting role exerted by the inorganic matrix on the embedded textile. While polymeric impregnation of multifilament textiles maximizes the mechanical response of FRCM, it also introduces an organic element into an otherwise fully inorganic composite and, accordingly, raises some concerns in terms of high temperature vulnerability of the material. In this paper, the influence of thermal preconditioning on the tensile properties of carbon FRCM in a cementitious mortar is investigated, with special regard to the role of epoxyimpregnation of the openmesh textile. Eight FRCM specimens are subjected to a 250minutelong thermal preconditioning up to 300∘C, and their mechanical behavior is assessed and compared with eight specimens in the control group. It is found that, unexpectedly, the greatest performance loss is associated with the control, as opposed to the epoxycoated, group.
2024
 Theory of elastic wave propagation in a fluidsaturated multiporous medium with multipermeability
[Articolo su rivista]
Pramanik, D.; Manna, S.; Nobili, A.
abstract
This paper establishes the concept of elastic wave propagation in a multiporous medium with different permeabilities by assuming there are n distinct pore fluid phases. The dynamic equation of motion of elastic wave propagation through this multiporous medium is derived based on Lagrangian mechanics. In this regard, the generalized form of mass coefficients and then the energy loss due to the fluid phases in terms of dissipation coefficients are presented for lowfrequency limits with the help of Darcy's Law of multiphases system. The elastic coefficients of the constitutive equation in terms of compliance matrix are identified using a series of Gedanken experiments. Some significant results regarding the compressional and rotational waves in a multiporosity medium are derived. The validation of the theory has been shown by comparing it with the existing theory of single and double porosity. It is observed that there are (n+1) compressional waves corresponding to solid and fluid phases, whereas only one rotational wave is associated with the solid phase. The concept of multiporosity theory can contribute to a deeper understanding of wave behaviour in a porous medium.
2023
 A mechanical model for thin sheet straight cutting in the presence of an elastic support
[Articolo su rivista]
Shugailo, T.; Nobili, A.; Mishuris, G.
abstract
We study the mechanics of sheet straight cutting in terms of a linear elastic fracture mechanics (LEFM) problem for a infinite thin elastic Kirchhoff plate partly supported by a Winkler foundation. The plate features a semiinfinite crack that is located at the edge of the supported zone and that is subjected to shear and bending loads, representing the action of the cutting tool (e.g. scissors blades). The fact that the plate is only partly supported by the foundation significantly complicates the analysis for it creates a nonsymmetric framework, both locally and globally. Yet, a semianalytical solution is obtained through casting the matrix Wiener–Hopf problem in terms of a pair of convolution integral equations defined on a semiinfinite domain. Stress intensity factors (SIFs) are obtained which converge to the known limits for a symmetric and skewsymmetric free plate. This analysis reveals the fundamental role played by the support in affecting the SIFs in an opposing manner, by enhancing/decreasing the symmetric/skewsymmetric components. Consequently, changing the support stiffness is capable of shifting the failure mechanism, from bending to shear. This observation may be taken advantage of when cutting materials which are more sensitive to either of these failure mechanisms. Also, it proves that the role of the support cannot be neglected when developing mechanical models of any cutting process.
2023
 Hierarchical composite coating for enhancing the tensile behaviour of textilereinforced mortar (TRM)
[Articolo su rivista]
Signorini, Cesare; Sola, Antonella; Nobili, Andrea
abstract
We describe a novel class of interfacefunctionalised textilereinforced mortar (TRM) composite materials reinforced with basalt and alkaliresistant glass multifilament textiles embedded in a commercially available hybrid limecement mortar, usually applied for masonry retrofitting. Spotlight is set on improving the mechanical (tensile) performance of the system through a scalable and easytoapply surface treatment for the dry textiles. The treatment consists in soaking the textiles in highlydiluted epoxy resin, to which rice husk ash (RHA) is later added, acting as pozzolanic filler. The resulting functionalised textiles exhibit remarkable adhesion with the matrix owing to the presence of RHA having high specific surface area and rich amorphous content. Three different RHA powders are assessed and their performance is compared to that of plain silica fume. The role of RHA milling is also discussed. The RHA/epoxy coating significantly improves the ultimate tensile strength and energy dissipation capability of the TRMs. In particular, for basalttextile reinforced composites, the mean tensile strength is three times as large as that of uncoated specimens, whereas the dissipated energy at failure is nearly four times as much. Furthermore, the surface treatment qualitatively changes the cracking pattern of the TRMs, for many diffused small cracks appear during tensile testing, and this provides evidence of effective stress distribution in the matrix as a result of superior interface adhesion.
2023
 Indentation of a free beam resting on an elastic substrate with an internal lengthscale
[Articolo su rivista]
Radi, E.; Nobili, A.; Guler, M. A.
abstract
The plane strain problem of a slender and weightless beamplate loaded by a transversal point force in unilateral contact with a couple stress elastic foundation is investigated. The study aims to explore the consequences of the material internal lengthscale on the contact mechanics. In particular, compatibility between the beam and the foundation surface demands that both displacement and rotation match along the contact line. To this aim, couple tractions are exchanged besides the traditional contact pressure until separation between the beam and the foundation occurs. The problem is formulated making use of the Green's functions for a point force and a point couple acting atop of a couple stress elastic halfplane. A pair of coupled integral equations is thus derived, that governs the distribution of contact pressure and couple tractions, with one of them being immediately solved to provide an explicit relation between the two unknowns. In this sense, we retrieve the concept of a mechanically equivalent action, as it is the case of the Kirchhoff shear for plates. The remaining integral equation sets a cubic eigenvalue problem, whose linear term accounts for the microstructure. Its numerical solution is sought by expanding the equivalent contact pressure in series of Chebyshev polynomials vanishing at the contact region ends points, namely the liftoff points, and then applying a collocation strategy. The contact length, the distributions of contact pressure and couple tractions under the beam and the shearing force and bending moment along the beam are then obtained as a function of the material characteristic length. Results clearly indicate that accounting for the material internal lengthscale is mainly realized through exchange of the couple tractions, in the lack of which results much resemble those of the classical solution. Specifically, greater contact lengths and a stronger focusing effect about the loading point are encountered, which become very significant when the contact length approaches the internal lengthscale.
2023
 Influence of severe thermal preconditioning on the bond between carbon FRCM and masonry substrate: Effect of textile preimpregnation
[Articolo su rivista]
Bertolli, V.; Signorini, C.; Nobili, A.; D'Antino, T.
abstract
Fabricreinforced cementitious matrix (FRCM) composites often include polymerimpregnated bundles to improve the exploitation of the textile mechanical properties. However, organic components may degrade when exposed to elevated temperature. In this paper, the bond behavior of a carbon FRCM applied to a masonry substrate and exposed to a thermal preconditioning up to 300 °C for 250 min is investigated. Tensile tests on the textile and flexural and compression tests on the mortar matrix, as well as singlelap direct shear tests of FRCMmasonry joints with bare and impregnated textiles, are performed. Results show that the polymeric impregnation improves the mechanical properties of the FRCM even after thermal preconditioning.
2023
 Mechanics of HighContrast Elastic Solids
Contributions from Euromech Colloquium 626
[Prefazione o Postfazione]
Altenbach, H.; Nobili, A.; Prikazchikov, D.
abstract
2022
 Characterization of biocompatible scaffolds manufactured by fused filament fabrication of poly(3hydroxybutyrateco3hydroxyhexanoate
[Articolo su rivista]
Volpini, Valentina; Giubilini, Alberto; Corsi, Lorenzo; Nobili, Andrea; Bondioli, Federica
abstract
We characterize poly(3hydroxybutyrateco3hydroxyhexanoate) (PHBH) scaffolds for tissue repair and regeneration, manufactured by threedimensional fused filament fabrication (FFF). PHBH belongs to the class of polyhydroxyalkanoates with interesting biodegradable and biocompatible capabilities, especially attractive for tissue engineering. Equally, FFF stands as a promising manufacturing technology for the production of customdesigned scaffolds. We address thermal, rheological and cytotoxicity properties of PHBH, placing special emphasis on the mechanical response of the printed material in a wide deformation range. Indeed, effective mechanical properties are assessed in both the linear and nonlinear regime. To warrant uniqueness of the material parameters, these are measured directly through digital image correlation, both in tension and compression, while experimental data fitting of finiteelement analyses is only adopted for the determination of the second invariant coefficient in the nonlinear regime. Mechanical data are clearly porosity dependent, and they are given for both the cubic and the honeycomb infill pattern. Local strain spikes due to the presence of defects are observed and measured: those falling in the range 70–100% lead to macrocrack development and, ultimately, to failure. Results suggest the significant potential attached to FFF printing of PHBH for customizable medical devices which are biocompatible and mechanically resilient.
2022
 Durability of fibrereinforced cementitious composites (FRCC) including recycled synthetic fibres and rubber aggregates
[Articolo su rivista]
Signorini, Cesare; Nobili, Andrea
abstract
We discuss mechanical performance of fibrereinforced cementitious composites under exposure to four aggressive environments, namely alkaline, saline, sulphuric acid and distilled water immersion. A standard commercial Portland cement based matrix is considered alongside its lightweight modification wherein quarzitic sand is partially replaced by recycled rubber crumbs. Also, virgin polypropylene fibres are contrasted to PP+PET blended fibres where the PET fraction is obtained from recycling food packaging waste. Performance is assessed in bending as well as in compression. We find that recycled based specimens perform surprisingly well and that exposure to the aggressive environments mainly affects the matrix and it is not necessarily more detrimental to the lightweight partially recycled phase. A oneway analysis of variance (ANOVA) confirms the statistical significance of the results, which fully support the idea that the adoption of a substantial recycled fraction in construction materials still allows for high performance and durability standards.
2022
 Experimental and Theoretical Investigation of the Mechanical Properties of PHBH Biopolymer Parts Produced by Fused Deposition Modeling
[Articolo su rivista]
Nobili, A.; Signorini, C.; Volpini, V.
abstract
The mechanical response of printed dogbone specimens of poly(3hydroxybutyrateco3hydroxyhexanoate) (PHBH) in linear and nonlinear regimes is investigated. Fused filament fabrication (FFF), also regarded as fused deposition modeling (FDM), is adopted to manufacture the PHBH elements. A compressible Mooney–Rivlin constitutive law is back fitted onto digital image correlation (DIC) data, as well as uniaxial tensile test data. Effective mechanical properties are given, which may be used to design and optimize the response of printed structures. Strain values at the verge of failure in tension are also experimentally obtained. Results are especially useful for modeling mechanical response of PHBH, which is an emerging biopolymer with promising application fields in biomedical engineering, through additive manufacturing techniques.
2022
 Frictionless contact problem between a loaded beam and a couple stress elastic halfplane
[Abstract in Atti di Convegno]
Radi, E; Nobili, A
abstract
2022
 Hamiltonian/Stroh formalism for anisotropic media with microstructure
[Articolo su rivista]
Nobili, Andrea; Radi, Enrico
abstract
Moving from variational principles, we develop the Hamiltonian formalism for generally anisotropic microstructured materials, in an attempt to extend the celebrated Stroh formulation. Microstructure is expressed through the indeterminate (or MindlinTiersten's) theory of couple stress elasticity. The resulting canonical formalism appears in the form of a Differential Algebraic system of Equations (DAE), which is then recast in purely differential form. This structure is due to the internal constraint that relates the micro to the macro rotation. The special situations of plain and antiplane deformations are also developed and they both lead to a 7dimensional coupled linear system of differential equations. In particular, the antiplane problem shows remarkable similarity with the theory of anisotropic plates, with which it shares the Lagrangian. Yet, unlike for plates, a classical Stroh formulation cannot be obtained, owing to the difference in the constitutive assumptions. Nonetheless, the canonical formalism brings new insight into the problem's structure and highlights important symmetry properties.
2022
 Highly Dissipative FiberReinforced Concrete for Structural Screeds
[Articolo su rivista]
Signorini, Cesare; Sola, Antonella; Malchiodi, Beatrice; Nobili, Andrea
abstract
Synthetic fibers, especially polypropylene (PP) fibers, are emerging as a viable reinforcement for concrete, on account of their excellent durability, affordability, antispalling capability, low density, and magnetic transparency. Yet, the chemical nature of PP hinders the development of strong bonds at the fibertomatrix interface, with negative effects on the mechanical performance. To overcome this difficulty, in this research fibers are either chemically attacked (etched) or coated through solgel nanosilica deposition in order to promote their affinity to the hydration products in the binder. Threepoint bending tests at different scales are carried out on unnotched specimens, including largescale beams consisting of PPreinforced concrete for structural screeds. Functionalization, especially in the form of silica coating, improves the binderfiber interaction, which is responsible for a remarkable increment in the specific energy dissipated at failure, with respect to untreated fibers. Most importantly, both surface treatments induce a substantial hardening response as opposed to the softening behavior that is characteristic of lowdosage fiberreinforced concrete. We conclude that surface functionalization, and especially nanosilica coating, offers significant advantages for better exploiting the reinforcing effect of PP fibers, and these carry over at different scales. In particular, results appear promising for screeds, which advocate optimal mechanical performance and durability while keeping the fiber content to a minimum.
2022
 Miscela per massetti alleggeriti contenente aggregati inerti generati dal recupero di campi sportivi
[Brevetto]
Signorini, Cesare; Nobili, Andrea; Volpini, Valentina
abstract
La presente invenzione si riferisce ad una miscela per massetti alleggeriti per la realizzazione di sottofondi non strutturali, sia per nuove costruzioni che per opere di restauro. Tale miscela è caratterizzata da una elevata capacità isolante termica, presentando infatti un basso coefficiente di conducibilità termica e una elevata permeabilità al vapore d’acqua. Sono note miscele per massetti realizzate con inerti naturali o sintetici, vergini o da riciclo. Tuttavia, tali miscele note presentano il problema di non consentire il reimpiego di materiale di recupero di natura polimerica ed elastomerica derivante dallo smaltimento di sottofondi in erba sintetica ad uso sportivo. Allo stato attuale, i suddetti materiali a fine vita, essendo di difficile reimpiego, sono destinati alla termovalorizzazione o al conferimento in discarica. Scopo della presente invenzione è quello di risolvere i suddetti problemi della tecnica anteriore fornendo una miscela per massetti alleggeriti che consenta di recuperare scarti plastici ed elastomerici, nonché sabbia minerale e macrofibre poliolefiniche, da fonti come i sottofondi in erba sintetica ad uso sportivo che, ad oggi, non trovano reimpiego alternativo a fine vita, evitandone il conferimento in discarica o alla valorizzazione termica. Un altro scopo della presente invenzione è quello di evitare trattamenti del rifiuto a monte dell’incorporazione nel premiscelato. Il materiale di riciclo, infatti, essendo di per sé inerte, viene esclusivamente recuperato e parzialmente suddiviso tramite semplice setacciamento, non necessitando di ulteriori trattamenti chimici più complessi e dispendiosi.
2022
 Performance of concrete reinforced with synthetic fibres obtained from recycling endoflife sport pitches
[Articolo su rivista]
Signorini, Cesare; Marinelli, Simona; Volpini, Valentina; Nobili, Andrea; Radi, Enrico; Rimini, Bianca
abstract
Microplastics pollution has risen at an alarming pace over the last decades and it is now recognised as a leading environmental emergency. Indeed, only a very small fraction of annual plastic production is successfully reused, while the vast majority is either disposed of (mainly through incineration or landfilling) or dispersed into the environment. In this paper, polyolefins synthetic fibres, obtained from processing disposed artificial turf pitches aimed at paving sport facilities, are studied. Focus is set on assessing their potential for the Fibre Reinforced Concrete (FRC) technology. Mechanical performance is discussed at two fibre volume fractions, namely 3% and 5% vol., alongside environmental impact. The former is assessed in bending and reveals a significant enhancement of the postcrack energy dissipation capability, whose extent is compatible with what is usually obtained by the adoption of virgin fibres. This is especially significant in consideration of the light processing operated on the waste material. Indeed, life cycle assessment is adopted to evaluate the environmental impact of fibre reuse against fibre manufacturing from either virgin materials or plastic waste. It clearly appears that fibre reuse brings a double environmental benefit: on the one side, it decreases the need for new plastics and, on the other, it reduces plastic waste, whose traditional disposal technique, through incineration, entails a considerable footprint.
2022
 Stoneley Waves in Media with Microstructure
[Relazione in Atti di Convegno]
Nobili, A.
abstract
The role of microstructure in affecting propagation of antiplane Stoneley waves, that are waves localized at the discontinuity surface between two perfectlybonded halfspaces, is considered. Microstructure is described within the linear theory of isotropic couple stress elastic materials with microinertia. The dispersion relation is a symmetric triterm combination of the Rayleigh functions in the relevant halfspace with a coupling term. In contrast to classical elasticity, where antiplane Stoneley waves are never supported and inplane waves exist only inasmuch as shear velocities for the halfspaces are close enough, it is found that propagation is largely possible, although it occurs beyond a cuton frequency. For the latter, an explicit expression is given alongside dispersion curves. These results may adopted in nextgeneration nondestructive testing (NDT) appliances to account for the material microstructure.
2022
 Stroh formulation of straingradient elasticity.
[Abstract in Atti di Convegno]
Nobili, A; Radi, E
abstract
2022
 Veering of Rayleigh–Lamb waves in orthorhombic materials
[Articolo su rivista]
Nobili, A.; Erbas, B.; Signorini, C.
abstract
We analyse veering of Rayleigh–Lamb waves propagating in a plane of elastic symmetry for a thin orthotropic plate. We demonstrate that veering results from interference of partial waves in a similar manner as it occurs in systems composed of onedimensional (1D) structures, such as beams or strings. Indeed, in the neighbourhood of a veering point, the system may be approximated by a pair of interacting tout strings, whose wave speed is the geometric average of the phase and group velocity of the relevant partial wave at the veering point. This complementary pair of partial waves provides the coupling terms in a form compatible with a action–reaction principle. We prove that veering of symmetric waves near the longitudinal bulk wave speed repeats itself indefinitely with the same structure. However, the dispersion behaviour of Rayleigh–Lamb waves are richer than that of 1D systems, and this reflects also on the veering pattern. In fact, the interacting tout string model fails whenever the dispersion branch is not guided by either partial wave. This often occurs when neighbouring veering points interact and partial waves no longer provide guiding curves.
2021
 Antiplane Stoneley waves propagating at the interface between two couple stress elastic materials
[Articolo su rivista]
Nobili, A.; Volpini, V.; Signorini, C.
abstract
We investigate antiplane Stoneley waves, localized at the discontinuity surface between two perfectly bonded halfspaces. Both halfspaces are elastic linear isotropic and possess a microstructure that is described within the theory of couple stress materials with microinertia. We show that the microstructure deeply affects wave propagation, which is permitted under broad conditions. This outcome stands in marked contrast to classical elasticity, where antiplane Stoneley waves are not supported and inplane Stoneley waves exist only under very severe conditions on the material properties of the bonded halfspaces. Besides, Stoneley waves may propagate only beyond a threshold frequency (cuton), for which an explicit expression is provided. For a given frequency above cuton, this expression lends the admissible range of material parameters that allows propagation (passband). In particular, significant contrast between the adjoining materials is possible, provided that Stoneley waves propagate at high enough frequency. Therefore, microinertia plays an important role in determining the features of propagation. Considerations concerning existence and uniqueness of antiplane Stoneley waves are given: it is found that evanescent and decaying/exploding modes are also admitted. Results may be especially useful when accounting for the microstructure in nondestructive testing (NDT) and seismic propagation.
2021
 Asymptotically consistent sizedependent plate models based on the couplestress theory with microinertia
[Abstract in Rivista]
Nobili, A.
abstract
Several beam and plate models have been recently developed in the literature to accommodate for sizedependence. These are usually obtained starting from a generalized continuum theory (such as the couplestress, straingradient or nonlocal theory or their modifications) and then deducing the governing equations through Hamilton's principle and ingenuous kinematical assumptions. This approach, originated by Kirchhoff, usually fails to reproduce the dispersion features of the equivalent 3D theory. Besides, it produces a variety of models, in dependence of the different assumptions, such as Kirchhoff's or Mindlin's. In contrast, in this paper we adopt asymptotic reduction: moving from the couplestress linear theory of elasticity with microinertia, we deduce new models for elongation and flexural deformation of microstructured plates. The resulting models are consistent, in the sense that they reproduce the dispersion features of the corresponding 3D body. Also, models are unique, for they may only differ by the order of the approximation. We find that microstructure especially affects inertia terms, which can be hardly captured by apriori kinematical assumptions. For static flexural deformations, our results match those already obtained assuming plane crosssections within the modified couplestress theory. In fact, we show that couplestress, reduced couplestress and strain gradient theories all lead to equivalent results. Higher order models are also given, that describe the near firstcutoff behaviour and account for thickness deformations in the spirit of Timoshenko.
2021
 Bounds to the pullin voltage of a mems/nems beam with surface elasticity
[Articolo su rivista]
Radi, E.; Bianchi, G.; Nobili, A.
abstract
The problem of pullin instability of a cantilever micro or nanoswitch under electrostatic forces has attracted considerable attention in the literature, given its importance in designing micro and nanoelectromechanical systems (MEMS and NEMS). The nonlinear nature of the problem supports the typical approach that relies on numerical or semianalytical tools to approximate the solution.
By contrast, we determine fully analytical upper and lower bounds to the pullin instability phenomenon for a cantilever beam under the action of electrostatic, van der Waals or Casimir forces. In particular, the novel contribution of this works consists in accounting for size effects analytically, in the spirit of surface elasticity, which adds considerable complication to the problem, allowing for a nonconvex beam deflection. Surface energy effects are generally ignored in classical elasticity. However they become relevant for nanoscale structures due to their high surface/volume ratio. Closed form lower and upper bounds are given for the pullin characteristics, that allow to discuss the role of several tuneable parameters. Indeed, the evolution of the cantilever tip deflection is presented as a function of the applied voltage up to the occurrence of pullin and the contribution of van der Waals and Casimir intermolecular interactions is discussed. It is found that intermolecular forces strongly decrease the pullin voltage, while surface elasticity works in the opposite direction and stabilizes the system. The accuracy of the bounding solutions is generally very good, given that upper and lower analytical bounds are very close to each other, although it decreases as the effect of surface elasticity becomes more pronounced. Finally, approximated closedform relations are developed to yield simple and accurate design formulae: in particular, they provide estimates for the minimum theoretical gap and for the maximum operable length for a freestanding cantilever in the presence of the effects of surface elasticity and intermolecular interactions. Results may be especially useful for designing and optimizing NEMS switches.
2021
 Comparing durability of steel reinforced grout (SRG) and textile reinforced mortar (TRM) for structural retrofitting
[Articolo su rivista]
Signorini, C.; Nobili, A.
abstract
We assess tensile performance of Steel Reinforced Grout (SRG) and Fabric Reinforced Cementitious Matrix/Textile Reinforced Mortar, upon exposure to aggressive environments. Galvanized and brasscoated Ultra High Tensile Strength Steel fabrics are considered for SRG, while carbon, ARglass, basalt and PBO fabrics are investigated for TRM, in a common cement mortar. Exposure to the aggressive environments is realized by specimen immersion for 1000 h (41.6 days) at controlled temperature in distilled water as well as alkaline, saline and acid solutions. Mechanical performance of rectangular 1ply coupons is assessed in uniaxial traction: Ultimate strength and elongation, dissipated energy at failure and environmental conversion factors for design values are calculated and compared. It is found that significant performance difference exists in dependence of the aggressive environment under consideration. As a result, careful selection of the reinforcing fabric leads to substantial advantage in terms of durability, that should be capitalized upon at the design stage. A simple material selection matrix is presented which suggests the best reinforcing textile/aggressive environment combination for design purposes.
2021
 Engineered Materials for Sustainable Structures
[Monografia/Trattato scientifico]
Frassine, Roberto; Nobili, Andrea; Saccomandi, Giuseppe; Signorini, Cesare
abstract
2021
 Epoxy Resins for Interphase Strengthening of TextileReinforced Composites for Structural Applications
[Capitolo/Saggio]
Signorini, C.; Nobili, A.
abstract
In the field of structural retrofitting and building rehabilitation, inorganic matrix textilereinforced composite materials offer many interesting advantages, such as resistance to high temperatures and aggressive environments, water vapor permeability, compatibility with traditional supports and reversibility of intervention. Yet, mechanical performance of the reinforcing system strongly depends on the bond quality at the fabrictomatrix interphase, which is usually unsatisfactory. Indeed, hydration products of the inorganic binder are incapable of penetrating among the multifilament yarn, thus allowing for the socalled telescopic failure. Therein, inner filaments (the core) slide over outer filaments (the sleeve). This failure mode occurs inconsistently and, although imparting ductility, prevents exploitation of the reinforcing potential of the fabric. In this chapter, we discuss a landscape of coating techniques intended to promote fabrictomatrix adhesion. Design parameters for the coating, such as formulation, viscosity and thickness, alongside an investigation of the system thermal stability, are discussed based on recent advances in the field.
2021
 Microstructured induced band pattern in Love wave propagation for novel nondestructive testing (NDT) procedures
[Articolo su rivista]
Nobili, A.; Volpini, V.
abstract
We propose a new approach for assessing microstructural properties of materials via nondestructive testing (NDT). This approach lies on the observation that, accounting for the microstructure within the materials, reveals a nonclassical band propagation pattern for Love waves. Precisely this propagation structure may be directly related to the internal microstructure. To illustrate this, propagation of Love waves is first investigated within the linear theory of couple stress materials with microinertia. Proving wave existence by the argument principle provides a closedform condition for propagation to occur. This connection defines propagation bands, whose limits correspond to the situation when Love waves move with the same speed as bulk waves in the underlying halfspace (internal resonance). This condition is closely related to the layertosubstrate microstructure and it may be used to assess either of the two. Furthermore, we show that the frequency equation is a threeterm combination of antiplane Rayleigh and Rayleigh–Lamb functions (in a free and in a free/clamped plate). Consequently, investigation of any extra observable, such as Rayleigh waves, reduces the risk of multiple solutions at the signal processing stage. We finally consider the limit as either the halfspace or the layer becomes classical elastic. We show that this unseemly bonding of dissimilar models, sometimes adopted in the literature, usually leads to inconsistencies.
2021
 Quasiadiabatic approximation for thermoelastic surface waves in orthorhombic solids
[Articolo su rivista]
Nobili, A.; Pichugin, A. V.
abstract
An asymptotic model for timeharmonic motion in fullycoupled linear thermoelastic orthorhombic materials is presented. The asymptotic approach takes advantage of the observation that the parameter expressing departure from the purely adiabatic regime is extremely small in practice. Consequently, the leading order bulk response turns out to be nondissipative, and is governed by the usual equations of elastodynamics with adiabatic material constants. In the case of isothermal stressfree boundary conditions, it is shown that thermoelastic interaction is dominated by a thermoelastic boundary layer. Hence, effective boundary conditions may be constructed, which duly account for the influence of this boundary layer and successfully describe dispersion and dissipation of surface waves to leading order. As an illustration, in the special case of an isotropic halfspace with free isothermal boundary conditions, we recover the asymptotic results by Chadwick and Windle (1964). Numerical comparison of the dispersion curves for surface waves in an orthorhombic halfspace shows excellent agreement between the exact fullycoupled thermoelastic problem and the corresponding quasiadiabatic approximation, even for relatively large wavenumbers.
2021
 Targeting functionalised carbon nanotubes at the interphase of Textile Reinforced Mortar (TRM) composites
[Articolo su rivista]
Signorini, C.; Nobili, A.
abstract
Tensile performance of textile reinforced inorganic matrix composites strongly depends on the matrixtofabric bond strength, that is the weak chain in the system. In this work, we investigate the role of multiwalled carbon nanotubes (MWCNT) dispersion in an amorphous silica nanocoating for ARglass and carbon fabric Textile Reinforced Mortar (TRM) composites. Two lime mortars are considered at 56day curing. Comparative mechanical testing in uniaxial tension show remarkable enhancements in terms of mean ductility, strength and energy dissipation capabilities. Besides, coating successfully hinders telescopic failure and delamination, which significantly narrows data scattering and benefits design limits. Crack pattern analysis reveals that coating promotes diffuse cracking in the specimen, with gradual and progressive damage buildup. Indeed, mean crack width and mean crack spacing are consistently reduced. BET, optical and ESEM microscopy supports the action mechanism of the coating, that promotes wettability, surface roughening and imparts a remarkable increase in the specific surface area of the reinforcement.
2020
 A new Rayleighlike wave in guided propagation of antiplane waves in couple stress materials
[Articolo su rivista]
Nobili, A.; Radi, E.; Signorini, C.
abstract
Motivated by the unexpected appearance of shear horizontal Rayleigh surface waves, we investigate the mechanics of antiplane wave reflection and propagation in couple stress (CS) elastic materials.
Surface waves arise by mode conversion at a free surface, whereby bulk travelling waves trigger inhomogeneous modes. Indeed, Rayleigh waves are perturbations of the travelling mode and stem from its reflection at grazing incidence. As well known, they correspond to the real zeros of the Rayleigh function.
Interestingly, we show that the same generating mechanism sustains a new inhomogeneous wave, corresponding to a purely imaginary zero of the Rayleigh function. This wave emerges from "reflection"
of a bulk standing mode: This produces a new type of Rayleighlike wave that travels away from, as opposed to along, the free surface, with a speed lower than that of bulk shear waves. Besides, a third zero of the Rayleigh function may exist, which represents waves attenuating/exploding both along and away from the surface. Since none of these zeros correspond to leaky waves, a new classification of the Rayleigh zeros is proposed. Furthermore, we extend to CS elasticity Mindlin’s boundary conditions, by which partial waves are identified, whose interference lends RayleighLamb guided waves. Finally, asymptotic analysis in the thinplate limit provides equivalent 1D models.
2020
 Designing epoxy viscosity for optimal mechanical performance of coated Glass Textile Reinforced Mortar (GTRM) composites
[Articolo su rivista]
Signorini, C.; Nobili, A.; Sola, A.; Messori, M.
abstract
Preliminary epoxy coating of the reinforcing fabric provides an effective approach for improving matrixtofabric strength in inorganic matrix composites. We investigate the effect of epoxy resin dilution in acetone on uniaxial tensile performance of coated alkaliresistant (AR) glass fabric embedded in a limebased matrix. Remarkably, it is found that dilution has a mixed effect on performance and this trend is consistently retrieved for strength, ductility and energy dissipation. Indeed, performance initially decays and then it suddenly raises to a level close to or even exceeding that of the undiluted specimens. It is postulated that this behaviour is caused by resin viscosity, that falls off exponentially with the dilution degree. Once a viscosity threshold is breached, epoxy is capable of penetrating inside the yarn and thereby prevents telescopic failure, that is the sliding of the outer over the inner glass filaments. Furthermore, the interphase surface area increases dramatically and this enhances performance and narrows scattering. Besides, optimal viscosity is reached at an unexpectedly high dilution degree, whence material cost is significantly reduced. A costtoperformance comparison of common strengthening technologies is presented, which shows that diluted epoxy composites score comparably to FRPs. It is concluded that epoxy coating optimization plays an important role in designing inorganic matrix composites.
2020
 Diffraction and Reflection of Antiplane Shear Waves in a Cracked Couple Stress Elastic Material
[Capitolo/Saggio]
Nobili, Andrea; Radi, Enrico; Mishuris, Gennady
abstract
We investigate the effect of a semiinﬁnite rectilinear crack on diffraction and reﬂection of antiplane shear waves in an elastic solid with microstructure. Waves are induced by moving shear traction vectors applied at the faces of the crack. The material behavior is described by the indeterminate theory of couple stress elasticity considering micro inertia. This elastic constitutive model accounts for the material microstructure and it is a special case of the micropolar theory; it was developed by Koiter [3] for the quasistatic regime and later extended by Eringen [1] to include dynamic effects. The fullﬁeld solution is obtained through integral transforms and the WienerHopf technique [5] and it may be used as a bulding block to solve general wave propagation problems in a cracked halfspace in antiplane deformation. The solution differs signiﬁcantly from the classical result given in [2] for isotropic elastic materials. Indeed, unlike classical elasticity, antiplane shear Rayleigh waves are supported in couple stress materials [4]. A complicated wave pattern appears which consists of entrained waves extending away from the crack, reﬂected Rayleigh waves, localized waves irradiating from and body waves scattered by the cracktip. Wave diffraction and interference brings an important contribution to the stress intensity factors originally presented in [6] in the static framework. Resonance is triggered when the applied loading is fed into the cracktip at Rayleigh speed and this result is conﬁrmed by the evaluation of the energy release rate.
2020
 Failure mechanism of silica coated polypropylene fibres for Fibre Reinforced Concrete (FRC)
[Articolo su rivista]
Signorini, C.; Sola, A.; Malchiodi, Beatrice; Nobili, A.; Gatto, A.
abstract
This work investigates the effect of a fast, acidcatalysed solgel silica nanocoating on the mechanical performance of drawwire Polypropylene (PP) fibres used as dispersed reinforcement in Fibre Reinforced Concrete (FRC). The failure mechanism is investigated. To this aim, the role of curing time is also considered. Mechanical performance is assessed in pullout and threepoint bending tests of unnotched beams. Coating deeply affects the postcracking behaviour of FRC, which shifts from brittle (plain concrete), to softening (uncoated) and finally to plasticsoftening (coated fibres). Remarkably, 28day curing improves over 8day curing in terms of energy dissipation capability for coated fibres only. This suggests that fibretomatrix bond enhancement moves the failure mechanism from delamination at the interface to failure in the interphase zone. In the former case, failure is inconsistent and occurs independently from the curing time while in the latter failure depends on the matrix quality.
2020
 On the solution of the purely nonlocal theory of beam elasticity as a limiting case of the twophase theory
[Articolo su rivista]
Mikhasev, G.; Nobili, A.
abstract
In the recent literature stance, purely nonlocal theory of elasticity is recognized to lead to illposed problems. Yet, we show that, for a beam, a meaningful energy bounded solution of the purely nonlocal theory may still be defined as the limit solution of the twophase nonlocal theory. For this, we consider the problem of free vibrations of a flexural beam under the twophase theory of nonlocal elasticity with an exponential kernel, in the presence of rotational inertia. After recasting the integrodifferential governing equation and the boundary conditions into purely differential form, a singularly perturbed problem is met that is associated with a pair of end boundary layers. A multiparametric asymptotic solution in terms of sizeeffect and local fraction is presented for the eigenfrequencies as well as for the eigenforms for a variety of boundary conditions. It is found that, for simply supported end, the weakest boundary layer is formed and, surprisingly, rotational inertia affects the eigenfrequencies only in the classical sense. Conversely, clamped and free end conditions bring a strong boundary layer and eigenfrequencies are heavily affected by rotational inertia, even for the lowest mode, in a manner opposite to that brought by nonlocality. Remarkably, all asymptotic solutions admit a well defined and energy bounded limit as the local fraction vanishes and the purely nonlocal model is retrieved. Therefore, we may define this limiting case as the proper solution of the purely nonlocal model for a beam. Finally, numerical results support the accuracy of the proposed asymptotic approach.
2020
 Optimal epoxy dilution for epoxycoated textile reinforced mortar (Trm): An experimental perspective
[Relazione in Atti di Convegno]
Signorini, C.; Nobili, A.; Sola, A.; Messori, M.
abstract
The effect of epoxy dilution with acetone on the mechanical performance of epoxycoated alkaliresistant glass (ARG) fabric embedded in a limebased mortar is studied experimentally. The mechanical behaviour of the composite system is assessed in uniaxial tensile tests, according to the ICC guidelines. Epoxy is diluted in acetone and several concentrations, namely 10%, 25%, 50%, 75% and 90%, are considered in an attempt to define a decay law for strength, ductility and dissipated energy at failure. Although epoxycoating promotes a striking improvement of the mechanical performance with respect to the uncoated specimens, epoxy dilution appears to little affect the global response, even at very low epoxytosolvent ratios. Actually, a notable increase in the ultimate strength and strain as well as dissipation capacity are evidenced for 75% dilution. Indeed, epoxy resin is able to uniformly impregnate the bundles of the yarns in a very thin layer, still preserving its contribution to the mechanical performance. In fact, wettability of the yarns plays a fundamental role in the mechanical performance of the laminate for it limitates telescopic failure. A threshold of viscosity is identified. Above this limit, the high quality of impregnation overcomes the issue of the reduction of the amount of epoxy resin in the coating. Besides, dilution strongly promotes the ease of application, as a result of the resin viscosity being sharply reduced. Most remarkably and contrarily to common expectation, the specific energy dissipated at failure exhibits a maximum point, whence an optimal dilution ratio exists which best balances interphase strength and ductility.
2019
 Diffraction and reflection of antiplane shear waves in a cracked couple stress elastic material
[Abstract in Atti di Convegno]
Nobili, A.; Radi, E.; Mishuris, G.
abstract
We investigate the effect of a semiinfinite rectilinear crack on diffraction and reflection of antiplane shear waves in an elastic solid with microstructure. Waves are induced by moving shear traction vectors applied at the faces of the crack. The material behavior is described by the indeterminate theory of couple stress elasticity considering micro inertia. This elastic constitutive model accounts for the material microstructure and it is a special case of the micropolar theory; it was developed by Koiter [3] for the quasistatic regime and later extended by Eringen [1] to include dynamic effects.
The fullfield solution is obtained through integral transforms and the WienerHopf technique [5] and it may be used as a bulding block to solve general wave propagation problems in a cracked halfspace in antiplane deformation. The solution differs significantly from the classical result given in [2] for isotropic elastic materials. Indeed, unlike classical elasticity, antiplane shear Rayleigh waves are supported in couple stress materials [4]. A complicated wave pattern appears which consists of entrained waves extending away from the crack, reflected Rayleigh waves, localized waves irradiating from and body waves scattered by the cracktip. Wave diffraction and interference brings an important contribution to the stress intensity factors originally presented in [6] in the static framework. Resonance is triggered when the applied loading is fed into the cracktip at Rayleigh speed and this result is confirmed by the evaluation of the energy release rate.
2019
 Diffraction of antiplane shear waves and stress concentration in a cracked couple stress elastic material with micro inertia
[Articolo su rivista]
Nobili, A.; Radi, E.; Wellender, A.
abstract
Scattering of waves impinging along a rectilinear semiillimitate crack is investigated in an elastic solid with microstructure under antiplane deformation. The material behavior is described by the indeterminate theory of couple stress elasticity. The propagation of Rayleigh waves is investigated first for, in contrast to classical elasticity, it may occur also in the absence of rotatory inertia. The fullfield solution is obtained through the WienerHopf technique and integral transform inversion. This solution provides dynamic stress intensity factors which appear as generalization of the corresponding results obtained in statics. Resonance, wave transmission and energy release rate are also discussed. Finally, it is shown that the maximum stress criterion can be hardly generalized in a timeharmonic framework.
2019
 Effect of high temperature exposure on epoxycoated glass textile reinforced mortar (GTRM) composites
[Articolo su rivista]
Messori, M.; Nobili, A.; Signorini, C.; Sola, A.
abstract
An experimental investigation on the mechanical performance of epoxycoated AlkaliResistant (AR) glass textile reinforced mortar subjected to elevated temperature is presented. Two epoxy coatings are considered, which differ by the hardening agent alone. After 56 days dry curing, specimens are heated up to four different temperatures. After cooling down to ambient temperature, specimens are assessed in uniaxial tensile test according to Annex A of AC434. First cracking strength and elongation, ultimate tensile strength and elongation, cracked and uncracked moduli, transition point location and energy dissipation capability are evaluated. It is found that, in the explored temperature range, degradation is surprisingly mild and strongly dependent on the resin which is taken as coating agent. Indeed, temperature exposure may lead to strength enhancement. This positive outcome takes place at the expense of ductility and it is traced back, through Differential Scanning Calorimetry (DSC), to a postcuring process. Nonetheless, energy dissipation still decreases with temperature and, remarkably, with the same powerlaw behaviour for both resins. Such behaviour is compatible with a cumulative Weibull distribution, that is adopted in thermal damage models for resins, and it indicates that the underlying damage mechanism indeed operates on the resin at the fabrictomatrix interface. (C) 2019 Elsevier Ltd. All rights reserved.
2019
 Limecement textile reinforced mortar (TRM) with modified interphase
[Articolo su rivista]
Signorini, Cesare; Sola, Antonella; Nobili, Andrea; Siligardi, Cristina
abstract
Background: Lack of interphase compatibility between the fabric and the matrix significantly impairs the loadbearing capacity of textile reinforced mortar (TRM). In this study, we consider the application of two inorganic surface coatings for enhancing the interphase bond properties. Methods: Either of two silicabased coatings, namely nano and microsilica, were applied to alkaliresistant glass (ARG) and to hybrid carbon–ARG woven fabric. Mechanical performance of TRM reinforced with the uncoated and the coated fabric was compared in uniaxial tensile tests. Results: Mechanical testing provides evidence of a remarkable enhancement in terms of ultimate strength and deformability for the coated specimens. This effect can be ascribed to the improved hydrophilicity of the fibers’ surface and to the activation of pozzolanic reaction at the interphase. In addition, penetration of nano and microparticles in the bundle of the textile yarns reduces the occurrence of telescopic failure.
2019
 Sustainable mineral coating of alkaliresistant glass fibres in textilereinforced mortar composites
for structural purposes
[Articolo su rivista]
Signorini, Cesare; Nobili, Andrea; Siligardi, Cristina
abstract
The mechanical performance of a silicabased mineral nanocoating applied to alkaliresistant glass textilereinforced
composite materials aimed at structural strengthening is investigated experimentally. The silica nanofilm is directly
applied to the alkaliresistant glass fabric by sol–gel deposition. Two lime mortars are adopted as embedding matrix,
which differ by the ultimate compressive strength and elongation. Uniaxial tensile tests of prismatic coupons are carried
out according to the ICC AC434 guidelines. Remarkable strength and ductility enhancements could be observed in the
silicacoated group, as compared to the uncoated group, for both mortar types. Digital image correlation, electron
scanning and optical microscopy provide evidence of improved interphase strength. Xray diffraction of the anhydrous
mortars brings out the role of the mineralogical composition of the embedding media on the overall bonding properties
of the composites. Consideration of design limits and energy dissipation capabilities reveals the crucial role of matrix
ductility in bringing the contribution of interphase enhancement to full effect. We conclude that best performance
requires optimizing the pairing between fabrictomatrix adhesion and matrix ductility
2019
 Timeharmonic analysis of antiplane crack in couple stress elastic materials
[Abstract in Atti di Convegno]
Radi, E; Nobili, A; Mishuris, G
abstract
The time harmonic response of a rectilinear and semiinfinite crack in a couple stress (CS) elastic solid under Mode III loading conditions is investigated in the present work. The fullfield solution of the dynamic crack problem obtained in [1] through Fourier integral transforms and the Wiener–Hopf technique is generalized here by considering more general loading conditions, consisting in arbitrary reduced stress and couple stress tractions applied at the crack faces.
The solution for quasistatic Mode III crack in indeterminate CS elastic materials was given in [2]. Later, the problem of steadystate Mode III crack propagation was investigated in [3]. In the present work, a travelling wave loading, applied in the form of generalized reduced tractions at the crack faces, is considered as the forcing term. As a result, a complex wave pattern appears, which differs significantly from the Mode III classical elastic solution. The results of the present analysis may be used as a building block to address, by means of superposition, the problem of arbitrary antiplane wave propagation in a cracked CS solid. Resonance is triggered when the applied loading is fed into the cracktip at Rayleigh speed. Elastodynamic stress intensity factors are given, which generalize the corresponding results presented in [2] for the qusistatic framework. They incorporate the effect of the applied loading frequency and thereby account for the interplay of the diffracted waves.
A remarkable wave pattern appears which consists of entrained waves extending away from the crack, reflected Rayleigh waves moving along the crack surfaces, localized waves irradiating from the cracktip and body waves scattered around the cracktip. Interestingly, the localized wave solution may be greatly advantageous for defect detection through acoustic emission.
2018
 Dispersion of elastic waves in a layer interacting with a Winkler foundation
[Articolo su rivista]
Erbaş, B.; Kaplunov, J.; Nobili, A.; Kılıç, G.
abstract
Dispersion of plane harmonic waves in an elastic layer interacting with a one or twosided Winkler foundation is analyzed. The longwave lowfrequency polynomial approximations of the full transcendental dispersion relations are derived for a relatively soft foundation. The validity of the conventional engineering formulation of a Kirchhoff plate resting on an elastic foundation is
investigated. It is shown that this formulation has to be refined near the cutoff frequency of bending waves. The associated near cutoff expansion is obtained for both cases. A simple explicit formula demonstrating veering of bending and extensional waves is presented for a onesided foundation.
2018
 Explicit formulation for the Rayleigh wave field induced by surface stresses in an orthorhombic halfplane
[Articolo su rivista]
Nobili, A.; Prikazchikov, Danila A.
abstract
We develop an explicit asymptotic model for the Rayleigh wave field arising in case of stresses prescribed on the surface of an orthorhombic elastic halfplane. The model consists of an elliptic equation governing the behaviour within the halfplane, with boundary values given on the halfplane surface by a wave equation. Consequently, propagation along the surface is entirely accounted for by the hyperbolic equation, which, besides, may be immediately recast in terms of the associated surface displacement. The model readily solves otherwise involved dynamic problems for prescribed surface stresses, and its effectiveness is demonstrated for the classical Lamb's problem, as well as for the steadystate moving load problem. The latter example shows that the proposed model is really obtained by perturbation around the steadystate solution for a load moving at the Rayleigh speed.
2018
 Mechanical performance and crack pattern analysis of aged Carbon Fabric Cementitious Matrix (CFRCM) composites
[Articolo su rivista]
Signorini, Cesare; Nobili, Andrea; Falope, Federico O.
abstract
We discuss the effect of environmental exposure on mechanical performance of impregnated Carbon Fabric Reinforced Cementitious Matrix (CFRCM) composite. Following the recently published ICCES AC434 guidelines, mechanical performance of prismatic composite specimens is determined on the basis of tensile uniaxial tests. Exposure to saline and alkaline aqueous solutions is considered at 28 as well as 60day curing time. Special emphasis is placed on crack pattern evaluation as a mean to gain better insight into matrix/fabric bond quality. To this aim, the evolution of the average crack spacing and of the average crack width is determined as a function of strain for all test environments and curing times. It is found that curing time plays a significant role in mitigating the detrimental effect of aggressive environments. Furthermore, the average crack spacing provides a very reliable measure of matrix/fabric bond degradation at all test stages.
2018
 Mechanical performance of epoxy coated ARglass fabric Textile Reinforced Mortar: Influence of coating thickness and formulation
[Articolo su rivista]
Messori, Massimo; Nobili, Andrea; Signorini, Cesare; Sola, Antonella
abstract
The mechanical performance of epoxy coated ARglass fabric reinforced composite is investigated. A threestage manufacturing process is considered, which involves fabric surface functionalization, liquid coating deposition and longterm setting and finally fabric embedment in the mortar matrix. Two epoxy coatings are considered, which only differ by the hardening agent. However, coating thickness is significantly diverse as a result of modified viscosity during liquid deposition. Performance is assessed in uniaxial tension as well as in threepoint bending and it is expressed in terms of strength curves, data dispersion, crack pattern and failure mechanism. Remarkably, despite being very similar, the analyzed coatings produce a significantly different performance, especially when data dispersion is incorporated and design limits are considered. Indeed, although both coatings are able to consistently deliver fabric rupture at failure, only the thinnest is associated with small data scattering and an almost plastic postpeak behavior in bending. The associated design elongation limit reaches the maximum allowed value according to the ICC guidelines. In fact, it appears that coating thickness plays a crucial role in determining mechanical performance and fabric flexibility. The proposed manufacturing process proves extremely effective at enhancing matrixtofabric adhesion and thereby prevent telescopic failure.
2018
 Silica coating for interphase bond enhancement of carbon and ARglass Textile Reinforced Mortar (TRM)
[Articolo su rivista]
Signorini, C.; Nobili, A.; Cedillo González, E. I.; Siligardi, C.
abstract
In this paper, we investigate the effect of silica nanocoating for interphase bond enhancement on the mechanical performance of Textile Reinforced Mortar (TRM) composite materials aimed at structural rehabilitation and strengthening. Alkaliresistant glass (ARG) and carbon fabric reinforcements are preliminarily treated via solgel deposition of SiO2coating to promote bond formation capability with the mortar matrix. Optical and electron microscopy provide evidence of interphase bond enhancement. Mechanical performance is assessed both in traction, through uniaxial elongation of prismatic coupons, and in flexure, by threepoint bending of laminated masonry bricks. Results are given in terms of mean strength curves, ultimate and design strength and strain values, cracked and uncracked moduli, mean crack spacing, mean crack width and energy dissipation. It is shown that mean absolute performance of silica coating offers a significant improvement over uncoated fabric, yet it is inferior to that of specimens which have been treated with a liquid partiallyorganic adhesion promoter (polymer coating). However, when design values are considered which incorporate the dispersion of experimental data, silica coating proves superior or at least equivalent to polymer coating, respectively for carbon and ARG fabric. These promising results describe the first application of silica nanocoating to fabric reinforced composite materials.
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.
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
 A robust approach for analysing dispersion of elastic waves in an orthotropic cylindrical shell
[Articolo su rivista]
Kaplunov, Julius; Nobili, Andrea
abstract
Dispersion of elastic waves in a thin orthotropic cylindrical shell is considered, within the framework of classical 2D KirchhoffLove theory. In contrast to direct multiparametric analysis of the lowest propagating modes, an alternative robust approach is proposed that simply requires evaluation of the evanescent modes (quasistatic edge effect), which, at leading order, do not depend on vibration frequency. A shortened dispersion relation for the propagating modes is then derived by polynomial division and its accuracy is numerically tested against the full KirchhoffLove dispersion relation. It is shown that the same shortened relation may be also obtained from a refined dynamic version of the semimembrane theory for cylindrical shells. The presented results may be relevant for modelling various types of nanotubes which, according to the latest experimental findings, possess strong material anisotropy.
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
 Impregnated Carbon Fabric–Reinforced Cementitious Matrix Composite for Rehabilitation of the Finale Emilia Hospital Roofs: Case Study
[Articolo su rivista]
Nobili, Andrea; Falope, FEDERICO OYEDEJI
abstract
In this paper, the mechanical performance of concrete beams strengthened by an impregnated carbon fabric–reinforced cementitious matrix (CFRCM) composite is investigated. The study is aimed at the rehabilitation of the Finale Emilia hospital roofs, which were severely damaged by the 2012 northern Italy earthquake. An 8mlong concrete beam was taken from the building for reinforcement and testing in a beam test setup. The composite is designed to be externally applied to the existing thin clay tile layer bonded to the concrete beam intrados. Two lamination cycles, which differ by the way in which the partially organic adhesion promoter is applied to the fabric, are considered. It was found that impregnation through fabric immersion provides a 1.5fold increase in the ultimate strength of the strengthened beam compared to expedited impregnation with a brush and that clay tiles make a very good supporting substrate, to the extent that cohesive fracture at the tile–concrete interface takes place on the verge of concrete failure near the hinge zone. Conversely, expedited impregnation of the carbon fabric with the adhesion promoter was unable to provide adequate fabric–matrix adhesion and led to delamination failure. Estimates of the adhesion strength, optimal bonded length, and of the composite, as well as of the concrete strain at failure, are provided.
2017
 Multiparametric analysis of strongly inhomogeneous periodic waveguideswith internal cutoff frequencies
[Articolo su rivista]
Kaplunov, J.; Nobili, Andrea
abstract
In this paper, we consider periodic waveguides in the shape of a inhomogeneous string or beam partially supported by a uniform elastic Winkler foundation. A multiparametric analysis is developed to take into account the presence of internal cutoff frequencies and strong contrast of the problem parameters. This leads to asymptotic conditions supporting nontypical quasistatic uniform or, possibly, linear microscale displacement variations over the highfrequency domain. Macroscale governing equations are derived within the framework of the FloquetBloch theory as well as using a highfrequencytype homogenization procedure adjusted to a string with variable parameters. It is found that, for the string problem, the associated macroscale equation is the same as that applying to a string resting on a Winkler foundation. Remarkably, for the beam problem, the macroscale behavior is governed by the same equation as for a beam supported by a twoparameter Pasternak foundation.
2017
 On the edgewave of a thin elastic plate supported by an elastic halfspace
[Relazione in Atti di Convegno]
Nobili, A.; Kaplunov, J.; Radi, E.; Tarantino, A. M.
abstract
In this contribution, we consider edgewave propagating in a thin elastic semiinfinite
plate which is bilaterally supported by a homogenenous isotropic elastic halfspace. The
problem is formulated in terms of a eigenproblem constituted by a system of five linear PDEs
in the plate transverse displacement and in the scalar and vector elastic potentials subject
to mixed boundary conditions accounting for platefundation displacement continuity under
the plate and zero normal stress outside. Zero tangential stress is envisaged throughout. The
problem could be reduced to an inhomogenenous WienerHopf functional equation in terms of
the halfspace surface displacement and of the platetofundation contact pressure only. The
kernel function is analyzed and the Rayleigh wave speed is obtained together with a novel
dispersion equation. Finally, kernel factorization is performed.
2017
 On the effect of curing time and environmental exposure on impregnated Carbon Fabric Reinforced Cementitious Matrix (CFRCM) composite with design considerations
[Articolo su rivista]
Nobili, Andrea; Signorini, Cesare
abstract
This paper investigates the effect of curing time and aggressive environmental exposure on the mechanical performance of impregnated Carbon Fabric Reinforced Cementitious Matrix (CFRCM) composite. Following the recently published IICES AC434 guidelines, saltwater, distilled water, alkali and acid resistance are investigated together with freezethaw cycles. Mechanical characterization is based on tensile uniaxial tests under deformation control of rectangularbase prismatic specimens. 28 and 60day curing times are considered for the control environment as well as for saltwater and alkali resistance. Deformation is monitored via digital acquisition. Besides uniaxial tests, experimental results comprise optical and scanning electron microscopy, crack pattern analysis and failure mechanism assessment. Focus is set on the determination of the design limits for the composite system at failure for the tested environments and curing times. In particular, a comparison is drawn with established design criteria already coded for FRP systems, which introduce the concept of safety (or partial) factors. Environmental conversion factors are also defined and calculated on a statistical basis in a twofold manner, as a mean to determine the design strain and strength limits of exposed specimens from the control (unexposed) data. It is found that they provide a convenient method for assessing the composite vulnerability to the aggressive environments at different curing times.
2017
 The edge waves on a Kirchhoff plate bilaterally supported by a twoparameter elastic foundation
[Articolo su rivista]
Kaplunov, Julius; Nobili, Andrea
abstract
In this paper, the bending waves propagating along the edge of a semiinfinite Kirchhoff plate resting on a twoparameter Pasternak elastic foundation are studied. Two geometries of the foundation are considered: either it is infinite or it is semiinfinite with the edges of the plate and of the foundation coinciding. Dispersion relations along with phase and group velocity expressions are obtained. It is shown that the semiinfinite foundation setup exhibits a cutoff frequency which is the same as for a Winkler foundation. The phase velocity possesses a minimum which corresponds to the critical velocity of a moving load. The infinite foundation exhibits a cutoff frequency which depends on its relative stiffness and occurs at a nonzero wavenumber, which is in fact hardly observed in elastodynamics. As a result, the associated phase velocity minimum is admissible only up to a limiting value of the stiffness. In the case of a foundation with small stiffness, asymptotic expansions are derived and beamlike onedimensional equivalent models are deduced accordingly. It is demonstrated that for the infinite foundation the related nonclassical beamlike model comprises a pseudodifferential operator.
2016
 Durability assessment of impregnated Glass Fabric Reinforced Cementitious Matrix (GFRCM) composites in the alkaline and saline environments
[Articolo su rivista]
Nobili, Andrea
abstract
In this paper, the effect of the alkaline and of the saline environments on prismatic specimens of impregnated alkaliresistant Glass Fabric Reinforced Cementitious Matrix (GFRCM) coupons is investigated. Two types of mortar are considered as representative of a midhigh performance or finetexture matrix. Coupons are manufactured, cured for 28 days and then submerged in the alkaline or saline solution at constant temperature in a climatic chamber for 1000 h (aging). Specimens in the control group are retained in the laboratory environment. Mechanical performance of the aged coupons is assessed through tensile testing. A Digital Image Correlation (DIC) system is used to measure the actual specimen deformation. Ultimate strength and elongation, uncracked and cracked matrix elastic moduli, turning point location and failure mechanisms are determined and compared with the control group's through a variance analysis. Statistical support is found for an important reduction in the ultimate strength and elongation, owing to mortar degradation. This result is confirmed by a similar analysis carried out on the single components (mortars and glass fabric) of the composite. Mortar degradation affects failure through favoring a less desirable fabric slip mechanism, as opposed to fabric rupture. © 2015 Elsevier Ltd. All rights reserved.
2016
 Edge wrinkling in elastically supported prestressed incompressible isotropic plates
[Articolo su rivista]
Destrade, Michel; Fu, Yibin; Nobili, Andrea
abstract
The equations governing the appearance of flexural static perturbations at the edge of a semiinfinite thin elastic isotropic plate, subjected to a state of homogeneous biaxial prestress, are derived and solved. The plate is incompressible and supported by a Winkler elastic foundation with, possibly, wavenumber dependence. Small perturbations superposed onto the homogeneous state of prestress, within the threedimensional elasticity theory, are considered. A series expansion of the plate kinematics in the plate thickness provides a consistent expression for the second variation of the potential energy, whose minimization gives the plate governing equations. Consistency considerations supplement a constraint on the scaling of the prestress so that the classical KirchhoffLove linear theory of prestretched elastic plates is retrieved. Moreover, a scaling constraint for the foundation stiffness is also introduced. Edge wrinkling is investigated and compared with body wrinkling. We find that the former always precedes the latter in a state of uniaxial prestretch, regardless of the foundation stiffness. By contrast, a general biaxial prestretch state may favour body wrinkling for moderate foundation stiffness. Wavenumber dependence significantly alters the predicted behaviour. The results may be especially relevant to modelling soft biological materials, such as skin or tissues, or stretchable organic thinfilms, embedded in a compliant elastic matrix. The research that led to the present paper was partially supported by a grant of the group GNFM of INdAM
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
 On lowfrequency vibrations of a composite string with contrast properties for energy scavenging fabric devices
[Articolo su rivista]
Kudaibergenov, Askar; Nobili, Andrea; Prikazchikova, Ludmilla
abstract
Free vibrations of a twocomponent string with highcontrast material parameters are considered at different boundary conditions to illustrate the very lowfrequency energy harvesting capability of fabric devices. It is revealed that, only for the case of mixed boundary conditions, lowfrequency (locally) almost rigidbody vibrations are admissible, provided that material parameter ratios lie in some well defined interval. A lowfrequency perturbation procedure is carried out to determine the eigenfrequencies as well as the eigenforms. The analysis is extended to a piecewise inhomogeneous string and to a string supported on an elastic foundation. It is shown that both situations may still admit lowfrequency vibrations, under certain restrictions on the material properties. This is particularly remarkable given that the situation of elastic support normally possesses two nonzero cutoff frequencies. The results may be especially relevant for energy scavenging fabric devices, where very lowfrequency (< 10 Hz) mechanical vibrations of textile fibers are harvested through friction.
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
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
 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
 On the generalization of the Timoshenko beam model based on the micropolar linear theory: Static case
[Articolo su rivista]
Nobili, Andrea
abstract
Three generalizations of the Timoshenko beam model according to the linear theory of micropolar elasticity or its special cases, that is, the couple stress theory or the modified couple stress theory, recently developed in the literature, are investigated and compared. The analysis is carried out in a variational setting, making use of Hamilton’s principle. It is shown that both the Timoshenko and the (possibly modified) couple stress models are based on a microstructural kinematics which is governed by kinosthenic (ignorable) terms in the Lagrangian. Despite their difference, all models bring in a beamplane theory only one microstructural material parameter. Besides, the micropolar model formally reduces to the couple stress model upon introducing the proper constraint on the microstructure kinematics, although the material parameter is generally different. Line loading on the microstructure results in a nonconservative force potential. Finally, the Hamiltonian form of the micropolar beam model is derived and the canonical equations are presented along with their general solution. The latter exhibits a general oscillatory pattern for the microstructure rotation and stress, whose behavior matches the numerical findings.
2015
 Pseudospectral methods in onedimensional magnetostriction
[Articolo su rivista]
Nobili, Andrea; Tarantino, Angelo Marcello
abstract
In this paper a pseudospectral method is proposed to solve a onedimensional model of a saturated hard ferromagnetic thinfilm structure within the Euler–Bernoulli kinematics. The model accounts for the nonlocal nature of the magnetoelastic coupling and interaction is in the form of a logarithmic potential. The proposed solution method adopts global polynomial interpolation at a main grid, given by the Gauss–Lobatto points, and it employs a secondary grid, consisting of the Gauss points, to perform the Gaussian quadrature. The two grids are nonoverlapping to avoid the singularity. Interpolation relates the unknowns, evaluated at the secondary grid, to their values at the collocation grid. Furthermore, the integration interval is parted about the singularity point. The procedure is assessed through the relative equilibrium residual for different values of the approximating polynomial degree and of the quadrature order. Maximum, average and standard deviation of the error are presented. An asymptotic analysis yields the Boundary Solution to the problem and results are compared when the latter is introduced in the numerical scheme. It is shown that its contribution is important in reducing the overall error. The equilibrium residual is plotted and its behavior discussed. It is further shown that numerical precision significantly affects the results at midspan, owing to the selfequilibrium of the system, thereby a limit exists to the best accuracy which may be gained through a more accurate interpolation.
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
 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 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
 Superposition principle for the tensionless contact of a beam resting on a winkler or a pasternak foundation
[Articolo su rivista]
Nobili, Andrea
abstract
A Green functionbased approach is presented to address the nonlinear tensionless contactproblem for beams resting on either a Winkler or a Pasternak twoparameter elastic foundation.Unlike the traditional solution procedure, this approach allows determination of the contact locus position independently from the deflection curves. By doing so, a general nonlinear connection between the loading and the contact locus is found, which enlightens the specific features of the loading that affect the position of the contact locus. It is then possible to build load classes sharing the property that their application leads to the same contact locus. Within such load classes, the problem is linear and a superposition principle holds. Several applications of the method are presented, including symmetric and nonsymmetric contact layouts, which can be hardly tackled within the traditional solution procedure. Whenever possible, resultsare compared with the existing literature. © 2013 American Society of Civil Engineers.
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
 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.
2012
 Variational Approach to Beams Resting on twoparameters tensionless elastic foundations
[Articolo su rivista]
Nobili, Andrea
abstract
This paper presents a Hamiltonian variational formulation to determine the energy minimizing boundary conditions (BCs) of the tensionless contact problem for an EulerBernoulli beam resting on either a Pasternak or a Reissner twoparameters foundation. It is shown that the BCs setting the contact loci are always given by second order homogeneous forms in the displacement and its derivatives. This stands for the nonlinear nature of the problem and calls for multiple solutions in the displacement, together with the classical result of multiple solutions in the contact loci position. In particular, it is shown that the Pasternak soil possesses an extra solution other than Kerr's, although it is proved that it must be ruled out owing to interpenetration. The homogeneous character of the BCs explains the wellknown load scaling invariance of the solutions. It is further shown that the Reissner foundation may be given two mechanical interpretations which lead to different BCs. Comparison with the established literature is drawn and numerical solutions shown which confirm the energy minimizing nature of the assessed BCs.
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.
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.
2009
 Mechanically induced HelfrichHurault effect in lamellar systems
[Articolo su rivista]
G., Napoli; NOBILI, Andrea
abstract
Layered phases are a common pattern of selforganization for several soft materials. These phases undergo buckling instability when subjected to dilatative strain: beyond a critical threshold, layers, initially flat, exhibit a periodical undulation. By using a continuum model, in a finite deformation framework, an expression for the critical threshold is provided, which differs from that predicted by the HelfrichHurault theory and yet it reverts to it in a thick specimen limit. With respect to the relevant literature, an analogous disagreement is found in the undulation amplitude expression as well. The obtained results appear particularly relevant when dealing with layered materials whose intrinsic coherence length is comparable to the cell thickness.
2008
 Magnetostriction of a hard ferromagnetic and elastic thinfilm structure
[Articolo su rivista]
Nobili, Andrea; Tarantino, Angelo Marcello
abstract
The magnetostriction of a thin film ferromagnetic and elastic structure is investigated.
2008
 Magnetostriction of a saturated hard ferromagnetic beamplate sandwich structure
[Articolo su rivista]
Nobili, Andrea
abstract
abstract
2007
 A hard ferromagnetic and elastic beamplate sandwich structure
[Articolo su rivista]
Nobili, Andrea; Tarantino, Angelo Marcello
abstract
In this paper, the deformation of a composite hard ferromagneticelastic beamplate structure is investigated. A sandwich structure, composed of two thin hard ferromagnetic layers, with a linear elastic layer in between, is considered. The deformation is due to the self generated magnetic field (magnetostriction). The aim is to assess the interaction forces among the perfectly bonded layers, through a consistent application of the classical nonlinear magnetoelastic theory. Once the general mechanical model is stated, the analysis is specialized to study longitudinal elongation, given its great relevance in technical applications. Owing to the nonlocal character of the magnetic action, a nonlinear integrodifferential equation is derived. Some qualitative properties of the solution are pointed out and the asymptotic behavior near the end sections is examined in detail. A finite differences approach allows writing an approximating nonlinear system of equations in the non asymptotic part of the solution, which is solved through a Newton's iterative scheme. The numerical results are discussed and it is shown how the asymptotic part of the solution well approximates the full behavior of the structure. Furthermore, the longitudinal interaction force density is found to be singular at the end crosssections, regardless of the assumed bonding type.
2007
 Finite homogeneous deformations of symmetrically loaded compressible membranes.
[Articolo su rivista]
Tarantino, Angelo Marcello; Nobili, Andrea
abstract
The nonlinear equilibrium problem of hyperelastic square membranes, stretched by dead loads, is investigated.
2007
 Improvement of superconvergence in Finite Element analysis
[Relazione in Atti di Convegno]
Mancuso, Massimo; Nobili, Andrea
abstract
Superconvergence
2007
 Instabilities in layered materials
[Relazione in Atti di Convegno]
G., Napoli; Nobili, Andrea
abstract
Stripe phases are a common pattern of selforganization forseveral soft materials. These materials are observed to undergobuckling instability when subjected to tensile stain. In this paper,buckling in layered materials is studied through the analysis of the EulerLagrange equation related to the deformation energy of the system. In the limiting case of thin cell,substantial differences are found with respect to the classical results obtained by Clarkand Meier \cite{ClMe73}. Furthermore,numerical analysis of a finite specimen of material is performed.
2007
 Magnetostriction in a hard ferromagnetic thinfilm beamplate theory
[Relazione in Atti di Convegno]
Nobili, Andrea
abstract
Magnetostriction is a remarkable nonlinear phenomenon which causes shape (and size) variations of a magnetized ferromagnet in response to different magnetic configurations. Its essence falls in the wide realm of magnetoelastic coupling and it is put to advantage in a wide array of technical applications. In fact, until recent times, nickel magnetostriction was successfully employed in sensing devices to capture acoustic and generally mechanical waves \cite[p.627ff]{Bozorth}. It was indeed by studying a Nickel sample that, in 1842, James Joule discovered magnetostriction. From the theoretical standpoint, magnetoelastic (and electroelastic) coupling provides an excellent example of a solid endowed with a vector microstructure \cite{Toupin, Brown2, Tiersten}. Yet microstructure, with its extra balance equations, is not the only interesting feature about magnetoelastic coupling. Indeed, microstructure interacts on a global scale, which means that a nonlocal theory is to be dealt with. Even more significant, owing to the nature of the magnetic phenomenon, the integral terms which account for the nonlocal character of the magnetic action may be improper or even singular (i.e. Cauchytype), inside the material body (they are indeed potentials). From this property stems a number of important consequences, ranging from the need of two vector fields to fully describe the magnetic action inside magnetized matter (often named magnetic induction and magnetic field) to a substantial change in the character of the tension vectortounit normal relation \cite{Brown2}.Although much study has been devoted to magnetoelastic coupling \cite{Brown1, Moonbook, Pao, Ogden}, its treatment provides outstanding difficulties both from the theoretical and from the numerical standpoint. For the most part, available solutions cover the case of the so called para or diamagnetic materials \cite{Moon,Wallerstein}, whose simplified magnetic constitutive law is responsible for different and conflicting force expressions \cite{Nobili,Zhou}. The greatest source of trouble is the nonlocal nature of the interaction mixed with the potentialtype nature of the integrals, which sets powerful numerical methods at a loss. In this contribution, a hard ferromagnetic thinfilm beamplate theory is described, whose greatest asset lies in leading to a system of ordinary nonlinear integrodifferential equations, which may be tackled through some carefully deployed numerical techniques \cite{Nobili2}.The model was originally developed in \cite{Nobili} for longitudinal elongations. The key step lays in matching the EulerBernoulli constrained kinematics with Maxwell equations in a layout where the magnetization vector is bound to follow the beamplate axis (latent microstructure). Such treatment allows both the mechanical and magnetic problem to be reduced to a onedimensional form. This outcome is obtained at the expense of letting the magnetization vector vary only along the longitudinal coordinate, which approximation, although severe from the domaintheory standpoint, is justified in a beamtheory spirit (and it is consistent with the traditional magnetic circuit approach). Furthermore, it allows involved constitutive laws to be dispensed with, whose major drawback lays in the difficulty of carrying through experimental results to numerically evaluate coupling coefficients.
2006
 Constitutive branching analysis of cylindrical bodies under inplane equibiaxial deadload tractions
[Articolo su rivista]
Tarantino, Angelo Marcello; Nobili, Andrea
abstract
Finite homogeneous deformations of hyperelastic cylindrical bodies subjected to inplane equibiaxial deadload tractions are analyzed. Four basic equilibrium problems are formulated considering incompressible and compressible isotropic bodies under plane stress and plane deformation condition. Depending on the form of the stored energy function, these plane problems, in addition to the obvious symmetric solutions, may admit asymmetric solutions. In other words, the body may assume an equilibrium configuration characterized by two unequal inplane principal stretches corresponding to equal external forces. In this paper, a mathematical condition, in terms of the principal invariants, governing the global development of the asymmetric deformation branches is obtained and examined in detail with regard to different choices of the stored energy function. Moreover, explicit expressions for evaluating critical loads and bifurcation points are derived. With reference to neoHookean, MooneyRiviin and OgdenBall materials, a broad numerical analysis is performed and the qualitatively more interesting asymmetric equilibrium branches are shown. Finally, using the energy criterion, a number of considerations are put forward about the stability of the computed solutions. (C) 2006 Elsevier Ltd. All rights reserved.
2005
 Unilateral contact problem for aging viscoelastic beams
[Articolo su rivista]
Nobili, Andrea; Tarantino, Angelo Marcello
abstract
The frictionless unilateral contact problem of a viscoelastic BernoulliEuler beam resting on a viscoelastic soil is studied. The mathematical formulation involves equilibrium equations, compatibility equations, and constitutive laws, with an aging integraltype form. The unilateral nature of the contact is imposed through a compatibility inequality, which allows the determination of the contact imprint at each time. Further, the governing integrodifferential equation for the unknown contact pressure is derived. As special cases, the elastic Winklertype soil and the rigid soil conditions are discussed. A numerical approach is presented, which employs the finite difference method along space and an adaptive stepbystep algorithm along time. The procedure allows for time discontinuities of both external loads and contact pressure. Several selected numerical examples are. presented and the influence of the most important material and geometrical parameters are shown. For the simplest situations, it was possible to compare the results obtained with known analytical solutions.
2001
 Exact deflection expressions for a thin solid circular plate loaded by periphery couples
[Articolo su rivista]
Nobili, Andrea; Strozzi, Antonio; Vaccari, Paolo
abstract
A mechanical analysis is carried out for a thin, solid, circular plate, deflected by a series of peripheryconcentrated couples with a radial or circumferential axis. Although such couples need not be of equal intensity or angularly equispaced, they must constitute a selfequilibrated system of couples. This problem is decomposed into a combination of two basic models, the first of which considers a single periphery couple with a radial axis, and the second addresses an edge couple with a circumferential axis. In both models the concentrated border couple is equilibrated by a sinusoidal boundary line load of proper intensity, whose wavelength equals the plate edge. When such basic configurations are combined, respecting the condition that the system of concentrated couples be selfequilibrated, the effects of the sinusoidal loads cancel out, and the title problem is recovered. A classical series solution in terms of purely flexural plate deflections is achieved for the two basic models, where the series coefficients are computed with the aid of an algebraic manipulator. For both models, the series is summed in analytical form over the whole plate region. Closedform deflection formulae can thus be easily derived from the two basic models for any combination of selfequilibrated edge couples, where some selected relevant situations are developed in detail.