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FEDERICO OYEDEJI FALOPE

Assegnista di ricerca
Dipartimento di Ingegneria "Enzo Ferrari"
Docente a contratto
Dipartimento di Giurisprudenza

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Pubblicazioni

2024 - Large twisting of non-circular cylinders in unconstrained elasticity [Articolo su rivista]
Falope, Federico; Lanzoni, Luca; Tarantino, Angelo Marcello
abstract

This paper deals with the equilibrium problem of non-circular cylinders subjected to finite torsion. A three-dimensional kinematic model is formulated, where, in addition to the rigid rotation of the cross sections, the large twist of the cylinder also generates in- and out-of-plane pure deformation of the cross sections and the variation of the cylinder length. Following the semi-inverse approach, the displacement field prescribed by the above kinematic model contains an unknown constant, which governs the elongation of the cylinder, and three unknown functions which describe the pure deformation of the cross sections. A Lagrangian analysis is then performed and the compressible Mooney-Rivlin law is assumed for the stored energy function. Once evaluated the Piola-Kirchhoff stresses, the boundary value problem is formulated. Nevertheless, the governing equations assume a coupled and nonlinear form which does not allow to apply standard solution methods. Therefore, the unknown functions are expanded into power series using polynomial terms in two variables. These series contain unknown constants which are evaluated applying the iterative Newton's method. With this procedure an accurate semi-analytical solution has been obtained, which can be used to compute displacements, stretches and stresses in each point of the cylinder. For the elliptical and rectangular sections, the results provided by the proposed solution method are shown by a series of graphs. Finally, the Poynting effect was investigated by varying the section shape of the cylinder.

2023 - Theoretical and experimental analysis of the von Mises truss subjected to a horizontal load using a new hyperelastic model with hardening [Articolo su rivista]
Pelliciari, Matteo; Falope, FEDERICO OYEDEJI; Lanzoni, Luca; Tarantino, Angelo Marcello
abstract

The von Mises truss has been widely studied in the literature because of its numerous applications in multistable and morphing structures. The static equilibrium of this structure was typically addresses by considering only geometric nonlinearities. However, Falope et al. (2021) presented an entirely nonlinear solution in finite elasticity and demonstrated that material nonlinearities play an important role in the prediction of both snap-through and Euler buckling. In such work, the von Mises truss was subjected to a vertical load and thus the system was symmetric and the deformations were relatively small. The present contribution extends the investigation to the case of a horizontal load, which is much more complex due to asymmetry and very large deformations. Since most rubbers employed in technological applications exhibit hardening under large stretches, we propose a new hyperelastic model capable of reproducing this behavior. The advantage of such model compared to the ones available in the literature is that the equilibrium solution maintains a straightforward mathematical form, even when considering compressibility of the material. In addition, in this work we present a new formulation in nonlinear elasticity to predict Euler buckling. The formulation takes into account shear deformation. The analytical prediction agrees well with both finite element (FE) and experimental results, thus demonstrating the accuracy of the proposed model.

2022 - 2D Green’s functions for an elastic layer on a rigid support loaded by an internal point force [Articolo su rivista]
Falope, Federico; Lanzoni, Luca; Radi, Enrico
abstract

The problem of a homogeneous isotropic elastic layer resting on a rigid base and loaded by an internal point force is analytically investigated under plane strain conditions. The displacement field is sought as the superposition of a fundamental solution (doublet state) and a homogeneous solution which allows satisfying the boundary conditions at the upper and lower boundaries of the layer. The displacement field is represented through convergent Fourier integral transforms. Once the closed form solution in the transformed domain is found, the displacement and stress fields are assessed by numerical inversion of transforms. Results concerning both the displacements and stresses for different positions of the load application point are reported and compared to FEM solution, finding very good agreement. The solutions obtained for horizontal and vertical point forces define the Green’s functions for the layer, which can be used to describe the mechanical interaction between the layer and an embedded body. As a striking application, the interaction between an elastic layer and an embedded laterally loaded wall or diaphragm is finally addressed, finding the contact pressure and, in turn, the internal forces in the diaphragm.

2022 - Analytical and experimental study of snap-through instability in truss structures [Abstract in Atti di Convegno]
Pelliciari, Matteo; Falope, FEDERICO OYEDEJI; Lanzoni, Luca; Tarantino, Angelo Marcello
abstract

Abstract

2022 - Finite Torsion of Compressible Circular Cylinders: An Approximate Solution [Articolo su rivista]
Falope, F. O.; Lanzoni, L.; Tarantino, A. M.
abstract

This paper deals with the equilibrium problem of circular cylinders under finite torsion. A three-dimensional kinematic model, where the large twisting of the cylinder is accompanied by transverse contraction and longitudinal extension, is formulated. Following a semi-inverse approach, the displacement field prescribed by the above kinematic model contains as unknowns the longitudinal displacement, the rigid rotation and the transverse stretch of cross sections. To simplify the mathematical formulation, the transverse stretch is assumed to be constant, as it radially undergoes very low variations. This hypothesis produces some approximations in the field equations, but the equilibrium solution obtained is however characterized by a satisfactory accuracy, as shown by the comparisons performed using the numerical techniques of the Finite Element Method (FEM). A Lagrangian analysis is performed and the compressible Mooney-Rivlin law is assumed for the stored energy function. Once evaluated the Piola-Kirchhoff stresses, the unknowns are determined by imposing the equilibrium conditions and the boundary conditions. For the end base of the cylinder two different boundary conditions have been considered, according to which the longitudinal translation of this surface is allowed or prevented. Once the kinematic unknowns have been determined, explicit formulae for displacements, stretches and stresses are provided, which show the role of the geometric and constitutive parameters, as well as of the twisting angle. The results provided by the proposed solution are shown by a series of graphs. The same torsion problem has been addressed with FEM. A very good agreement was found between the results obtained with the two different analyses. Finally, the nonlinear torsion problem was linearized by introducing the hypothesis of smallness of the displacement and deformation fields. With this linearization, the classical solution for the infinitesimal torsion problem was fully retrieved.

2022 - Finite bending of non-slender beams and the limitations of the Elastica theory [Articolo su rivista]
Falope, FEDERICO OYEDEJI; Lanzoni, Luca; Tarantino, Angelo Marcello
abstract

The problem of slender solids under finite bending has been addressed recently in Lanzoni and Tarantino (2018). In the present work, such a model is extended to short solids by improving the background formulation. In particular, the model is refined by imposing the vanishing of the axial force over the cross sections. The geometrical neutral loci, corresponding to unstretched and unstressed surfaces, are provided in a closed form. Two approximations of the models are obtained linearising both kinematics and constitutive law and kinematics only. It is shown that the approximations of the model, corresponding to the Euler Elastica formulation, can lead to significant values of the axial stress resultants despite pure bending conditions. For a generic form of compressible energy function, a nonlinear moment–curvature relation accounting for both material and geometric nonlinearities is provided and then specialised for a Mooney–Rivlin material. The obtained results are compared with simulations of 3D finite element models providing negligible errors. The normalisation of the moment–curvature relation provides the dimensionless bending moment as a function of the Eulerian slenderness of the solid. This dimensionless relation is shown to be valid for any aspect ratio of the bent solid and, in turn, it highlights the limitations of the Elastica arising in case of large deformations of solids.

2022 - Finite torsion of compressible hyperelastic cylinders: from simple to restrained torsion [Abstract in Atti di Convegno]
Falope, Federico; Lanzoni, Luca; Tarantino, Angelo Marcello
abstract

Abstract

2022 - Green functions for an elastic layer on a rigid base and related problems [Abstract in Atti di Convegno]
Falope, FEDERICO OYEDEJI; Lanzoni, Luca; Radi, Enrico
abstract

Abstract

2021 - Dispositivo per l'isolamento di apparecchiature industriali, strutture e infrastrutture civili basato su moduli reticolari a traliccio [Brevetto]
Falope, FEDERICO OYEDEJI; Lanzoni, Luca; Pelliciari, Matteo; Tarantino, Angelo Marcello; Salardi, Enrico
abstract

2021 - On the anticlastic bending of solids at finite strains [Abstract in Atti di Convegno]
Falope, Fo; Lanzoni, L; Tarantino, Am
abstract

The present work deals with the problem of compressible isotropic hyperelastic solids under finite bending. The problem is fully nonlinear and, conversely to the classical Rivlin solution [1], it is formulated in the framework of three-dimensional kinematics involving both large displacements and strains according to the context of finite elasticity. The model entails three kinematic assumptions, which stand for the planarity of the cross sections (Bernoulli-Navier hypothesis), the invariance of the curvature along the longitudinal direction of the solid (uniform bending) and the curvature of the cross sections (anticlastic curvature), that is assumed constant along the width of the solid [2]. Based on the semi-inverse approach and according to the kinematic assumptions, the 3D displacement field is found, and, in turn, the deformation gradient is assessed. Then, the equilibrium conditions, specialized for a compressible Mooney-Rivlin material, provide proper relations among the unknown kinematic parameters, thus leading to the closure of the problem. Emphasis in placed on the “moment-curvature relation”, which is found to be governed by two independent dimensionless parameters: the Eulerian slenderness and the compactness index of the solid cross sections [3]. Similarity is observed with respect the previous works of Lamb (1890) regarding the mechanical response of bent plates and the experiments performed by Searle (1933) as well. Moreover, such an analysis allows broadening the “Elastica” to the more general context of finite elasticity. In this work, the main results provided by the theoretical model are compared with those obtained by FE simulations and an experimental investigation based on a specifically designed mechanical apparatus, founding good agreement also for the case of extremely inflexed solids.

2021 - Snap-through and Eulerian buckling of the bi-stable von Mises truss in nonlinear elasticity: A theoretical, numerical and experimental investigation [Articolo su rivista]
Falope, F. O.; Pelliciari, M.; Lanzoni, L.; Tarantino, A. M.
abstract

In this paper, the equilibrium and stability of the von Mises truss subjected to a vertical load is analyzed from theoretical, numerical and experimental points of view. The bars of the truss are composed of a rubber material, so that large deformations can be observed. The analytical model of the truss is developed in the fully nonlinear context of finite elasticity and the constitutive behavior of the rubber is modeled using a Mooney–Rivlin law. The constitutive parameters are identified by means of a genetic algorithm that fits experimental data from uniaxial tests on rubber specimens. The numerical analysis is performed through a finite element (FE) model. Differently from the analytical and FE simulations that can be found in the literature, the models presented in this work are entirely developed in three-dimensional finite elasticity. Experiments are conducted with a device that allows the rubber specimens to undergo large axial deformations. For the first time, snap-through is observed experimentally on rubber materials, showing good agreement with both theoretical and numerical results. Further insights on Eulerian buckling of the rubber specimens and its interaction with the snap-through are given. A simple formulation to determine the critical load of the truss is presented and its accuracy is validated through experimental observation. Comparisons with a linear elasticity based approach demonstrate that an accurate prediction of snap-through and Eulerian buckling requires nonlinear formulations, such as the ones proposed in this work.

2021 - Snap-through and Eulerian buckling of the von Mises truss [Relazione in Atti di Convegno]
Pelliciari, Matteo; Falope, FEDERICO OYEDEJI; Lanzoni, Luca; Tarantino, Angelo Marcello
abstract

2021 - Snap-through of a bi-stable truss in finite elasticity [Relazione in Atti di Convegno]
Pelliciari, M.; Falope, F. O.; Lanzoni, L.; Tarantino, A. M.
abstract

2020 - Buckling of a Timoshenko beam bonded to an elastic half-plane: Effects of sharp and smooth beam edges [Articolo su rivista]
Falope, FEDERICO OYEDEJI; Lanzoni, Luca; Radi, Enrico
abstract

The problem of a compressed Timoshenko beam of finite length in frictionless and bilateral contact with an elastic half-plane is investigated here. The problem formulation leads to an integro-differential equation which can be transformed into an algebraic system by expanding the rotation of the beam cross sections in series of Chebyshev polynomials. An eigenvalue problem is then obtained, whose solution provides the buckling loads of the beam and, in turn, the corresponding buckling mode shapes. Beams with sharp or smooth edges are considered in detail, founding relevant differences. In particular, it is proofed that beams with smooth edges cannot exhibit a rigid-body buckling mode. A characteristic value of the stiffness ratio dimensionless parameter has been found for sharp edges, under which without loss of reliability, an analytic buckling load formula is provided. Finally, in agreement with the Galin solution for the rigid flat punch on a half-plane, a simple relation between the half-plane elastic modulus and the Winkler soil constant is found. Thus, a straightforward formula predicting the buckling loads of high stiff beams resting on elastic compliant substrates is proposed.

2020 - Dispositivo smorzatore assiale ad elastomeri [Brevetto]
Falope, FEDERICO OYEDEJI; Pelliciari, Matteo; Lanzoni, Luca; Tarantino, Angelo Marcello; Salardi, Enrico
abstract

2020 - FE Analyses of Hyperelastic Solids under Large Bending: The Role of the Searle Parameter and Eulerian Slenderness [Articolo su rivista]
Falope, Federico; Lanzoni, Luca; Tarantino, Marcello
abstract

A theoretical model concerning the finite bending of a prismatic hyperelastic solid has been recently proposed. Such a model provides the 3D kinematics and the stress field, taking into account the anticlastic effects arising in the transverse cross sections also. That model has been used later to extend the Elastica in the framework of finite elasticity. In the present work, Finite Element (FE) analyses of some basic structural systems subjected to finite bending have been carried out and the results have been compared with those provided by the theoretical model performed previously. In the theoretical formulation, the governing equation is the nonlinear local relationship between the bending moment and the curvature of the longitudinal axis of the bent beam. Such a relation has been provided in dimensionless form as a function of the Mooney–Rivlin constitutive constants and two kinematic dimensionless parameters termed Eulerian slenderness and compactness index of the cross section. Such parameters take relevance as they are involved in the well-known Searle parameter for bent solids. Two significant study cases have been investigated in detail. The results point out that the theoretical model leads to reliable results provided that the Eulerian slenderness and the compactness index of the cross sections do not exceed fixed threshold values.

2019 - Bending device and anticlastic surface measurement of solids under large deformations and displacements [Articolo su rivista]
Falope, F. O.; Lanzoni, L.; Tarantino, A. M.
abstract

Large bending of elastic bodies gives rise to significant transverse effects. Based on a recent theoretical model in the context of finite elasticity, both the longitudinal and anticlastic curvatures in bent solids under large deformation and displacement can be accurately assessed. In order to experimentally investigate the anticlastic deformation induced by large inflexion and corroborate the theoretical predictions, a properly designed mechanical bending device is here proposed. By imposing a rotation at the ends of the sample, both the longitudinal and anticlastic curvatures are measured by DIC (digital image correlation) monitoring instrumentation and compared with the theoretical results, finding good agreement. Compact analytical formulae for assessing the radii of curvature within the thickness of the sample are provided. Conversely to existing studies of the anticlastic surface induced by infinitesimal bending, the present analysis takes into account large through-to-thickness curvature variations, whose knowledg can plays a key role for a wide class of mechanical applications.

2019 - Finite bending of beams with anticlastic effect: analytical model, experimental test and FE modeling [Abstract in Atti di Convegno]
Falope, FEDERICO OYEDEJI; Lanzoni, Luca; Tarantino, Angelo Marcello
abstract

A recent model of a bent solid in finite elasticity appears in Literature [1]. Making reference to a compressible Mooney-Rivlin material, such a model is able to describe properly the anticlastic effect arising in a bent beam made of a rubber-like material. An experimental device is here presented (see Figure 1) aimed at simulating pure bending. In particular, the device lets the specimen free to exhibit its own elastic retaining force. Accordingly, the bent sample assumes the shape of an arc of circumference. With the aid of a DIC optical monitoring system, the experimental displacement field is acquired during the deformation process varying the angles imposed at the final beam cross sections. For different rubber specimens, based on a theoretical model [2], both compression and tensile tests have been performed in order to properly characterize the constitutive parameters. Once the constitutive parameters have been found, by means of non-linear fitting experimental data, a FE model has been carried out in order to reproduce the experimental test. A good agreement is found among analytical, experimental and numerical results, thus showing the reliability of the proposed experimental device together with the consistency of the basic hypotheses of the theoretical model.

2019 - The Bending Theory of Fully Nonlinear Beams [Monografia/Trattato scientifico]
Tarantino, A. M.; Lanzoni, L.; Falope, F. O.
abstract

This book presents the bending theory of hyperelastic beams in the context of finite elasticity. The main difficulties in addressing this issue are due to its fully nonlinear framework, which makes no assumptions regarding the size of the deformation and displacement fields. Despite the complexity of its mathematical formulation, the inflexion problem of nonlinear beams is frequently used in practice, and has numerous applications in the industrial, mechanical and civil sectors. Adopting a semi-inverse approach, the book formulates a three-dimensional kinematic model in which the longitudinal bending is accompanied by the transversal deformation of cross-sections. The results provided by the theoretical model are subsequently compared with those of numerical and experimental analyses. The numerical analysis is based on the finite element method (FEM), whereas a test equipment prototype was designed and fabricated for the experimental analysis. The experimental data was acquired using digital image correlation (DIC) instrumentation. These two further analyses serve to confirm the hypotheses underlying the theoretical model. In the book’s closing section, the analysis is generalized to the case of variable bending moment. The governing equations then take the form of a coupled system of three equations in integral form, which can be applied to a very wide class of equilibrium problems for nonlinear beams.

2019 - The bending of fully nonlinear beams. Theoretical, numerical and experimental analyses [Articolo su rivista]
Falope, Federico; Lanzoni, Luca; Tarantino, Angelo Marcello
abstract

This paper deals with the equilibrium problem of fully nonlinear beams in bending by extending the model for the anticlastic flexion of solids recently proposed by Lanzoni and Tarantino (2018) in the context of finite elasticity. In the first part of the paper it is shown, through a parametric analysis, that some geometrical parameters of the displacement field lose importance when slender beams are considered. Therefore, kinematics is reformulated and, subsequently, a fully nonlinear theory for the bending of slender beams is developed. In detail, no hypothesis of smallness is introduced for the deformation and displacement fields, the constitutive law is considered nonlinear and the equilibrium is imposed in the deformed configuration. Explicit formulas are obtained which describe the displacement fields of the inflexed beam, the stretches and the stresses for each point of the beam using both the Lagrangian and Eulerian descriptions. All these formulas are linearized by retrieving the classical formulae of the infinitesimal bending theory of beams. In the second part of the paper the theoretical results are compared with those provided by numerical and experimental analyses developed for the same equilibrium problem with the aim of justify the hypotheses underlying the theoretical model. The numerical model is based on the finite element (FE) method, whereas a test equipment prototype is designed and manufactured for the experimental analysis.

2018 - Double lap shear test on steel fabric reinforced cementitious matrix (SFRCM) [Articolo su rivista]
Falope, F. O.; Lanzoni, L.; Tarantino, Angelo Marcello
abstract

The present work deals with the experimental characterization of the mechanical behaviour of a galvanized steel fabric reinforced cementitious matrix (SFRCM).

2018 - 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 ICC-ES AC434 guidelines, mechanical performance of prismatic composite specimens is determined on the basis of tensile uni-axial tests. Exposure to saline and alkaline aqueous solutions is considered at 28- as well as 60-day 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 - Modified hinged beam test on steel fabric reinforced cementitious matrix (SFRCM) [Articolo su rivista]
Falope, F. O.; Lanzoni, L.; Tarantino, A. M.
abstract

An experimental campaign based on modied hinged beam test (MhBT) set-up has been reported in the present study. The samples consist of two concrete blocks coupled by a proper hinge device and laminated with steel wire fabrics embedded in a cementitious mortar layer. Two kinds of fabrics, made of galvanized steel strands with dierent mesh spacing, have been used to reinforce the concrete joists. With the aid of a DIC monitoring system, slippage prole at the interface between the concrete support and the mortar laminate along the contact region has been assessed, together with the fracture opening. Force vs slippage at the interface has been retrieved for the sampled tested according to the MhBT set-up. With the aim to obtain predictive ultimate load design formulas, a novel classication of laminate here proposed will be argued and related to a MhBT design formula. The in influence of peel and shear stresses interaction on the ultimate strength of the system has been discussed in detail.

2018 - Shear deformable beams in contact with an elastic half-plane [Abstract in Atti di Convegno]
Falope, F. O.; Lanzoni, L.; Radi, E.
abstract

The present work deals with the contact problem of a Timoshenko beam bonded to an elastic semi-infinite substrate under different loading conditions. The analysis allows investigating the effects induced by shear compliance of the beam, the stress intensity factors ad the beam edges as well as the singular nature of the interfacial stresses.

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 8-m-long 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 1.5-fold 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.

2016 - Euler-Bernoulli nanobeam welded to a compressible semi-infinite substrate [Articolo su rivista]
DI MAIDA, Pietro; Falope, FEDERICO OYEDEJI
abstract

The contact problem of an Euler-Bernoulli nano-beam of finite length bonded to a homogeneous elastic half plane is studied in the present work. Both the beam and the half plane are assumed to display a linear elastic behaviour under infinitesimal strains. The analysis is performed under plane strain condition. Owing to the bending stiffness of the beam, shear and peeling stresses arise at the interface between the beam and the substrate within the contact region. The investigation allows to evaluate the role played by the Poisson ratio of the half plane (and, in turn, its compressibility) on the beam-substrate mechanical interaction. Different symmetric as well as skew-symmetric loading conditions for the beam are considered, with particular emphasis to concentrated transversal and horizontal forces and couples acting at its edges. It is found that the Poisson ratio of the half plane affects the behaviour of the interfacial stress field, particularly at the beam edges, where the shear and peel stresses are singular.

2016 - Finite Thin Cover on an Orthotropic Elastic Half Plane [Articolo su rivista]
Falope, FEDERICO OYEDEJI; Radi, Enrico
abstract

The present work deals with the mechanical behaviour of thin films bonded to a homogeneous elastic orthotropic half plane under plain strain condition and infinitesimal strain. Both the film and semi-infinite substrate display linear elastic orthotropic behaviour. By assuming perfect adhesion between film and half plane together with membrane behaviour of the film, the compatibility condition between the coating and substrate leads to a singular integral equation with Cauchy kernel. Such an equation is straightforwardly solved by expanding the unknown interfacial stress in series of Chebyshev polynomials displaying square-root singularity at the film edges. This approach allows handling the singular behaviour of the shear stress and, in turn, reducing the problem to a linear algebraic system of infinite terms. Results are found for two loading cases, with particular reference to concentrated axial forces acting at the edges of the film. The corresponding mode II stress intensity factor has been assessed, thus providing the stress concentrations at both ends of the covering. Possible applications of the results here obtained range from MEMS, NEMS, and solar Silicon cell for energy harvesting to welded joint and building foundation.

2016 - Thin film bonded to elastic orthotropic substrate under thermal loading [Articolo su rivista]
Falope, FEDERICO OYEDEJI; Lanzoni, Luca; Radi, Enrico; Tarantino, Angelo Marcello
abstract

The problem of thin elastic films bonded on an elastic orthotropic substrate under thermal load is investigated in this work. Differently from past studies on the same topic, the effects induced by anisotropic behavior of the elastic substrate will be taken into account. Particular attention will also be paid to the determination of the displacement and stress fields induced by thermal loading. In particular, it is assumed that the thin films are deposed on the substrate at high temperature, and then the mismatch occurring during the cooling process, due to the difference between the thermal expansion coefficients of the two materials, is responsible for the permanent deformation assumed by the system. This phenomenon can be exploited for realizing a crystalline undulator. To this aim, the permanent deformation must be optimized in order to encourage the channeling phenomenon. By imposing equilibrium conditions and perfect adhesion between the film and the substrate, a singular integral equation is derived. A closed-form solution is achieved by expanding the interfacial shear stress fields in Chebyshev series. The unknown coefficients in the series expansion are then determined by transforming the integral equation into an infinite algebraic system.

2015 - Partially coated ceramic layer under thermal stress [Relazione in Atti di Convegno]
Falope, FEDERICO OYEDEJI; Lanzoni, Luca; Radi, Enrico
abstract

Thin films and coatings technology has known a large development in the last decades due to the large number of devices involving thin films employed in high-tech industries, mainly in microelectronics, electrochemistry, semiconductors and optical electronics. Indeed, realization of MEMS and NEMS used into biomedical components, chemical reactors, integrated circuit, solar cells, flat panels displays, sensors, insulator and protection systems, transducers, high-precision measuring instruments, etc. are examples of important applications having significant commercial implication. Recently, many theoretical and experimental studies have been focused on the feasibility of a crystalline undulator (CU), that is a special kind of MEMS realized by covering a ceramic substrate. This micro-device can be used to produce a coherent beam of X-ray at high energy levels by exploiting the channelling phenomenon [1]. The substrate generally consists of a Silicon or Germanium crystalline plate covered by a thin film deposed on both surfaces by a proper chemical process (e.g. LPCVD) at high temperature. Through a suitable photolitho-graphic process, the film is properly patterned in order to impart a periodic deformation to the crystalline substrate, suitable to produce coherent interaction with a beam particles. The system adopts a periodic curvature as a result of the misfit strain due to the different thermal expansivities of the layer and the film The present work provides an extension of the paper [2] by taking into account the anisotropy of the substrate and coatings. The substrate is modelled as a 2D orthotropic elastic layer under plane strain conditions, whereas the film is assumed to behave like a membrane, thus neglecting its flexural stiffness. The problem is formulated by imposing perfect adhesion between the film and the substrate, thus leading to a singular integral equation. The problem can be reduced to a linear algebraic system by using a series expansion of Chebyshev polynomials for the interfacial shear stress and Fourier series expansion for the displacement field. The effects of anisotropy of the materials are then examined and discussed.