Frédéric Lebon

Interfacial waves between piezoelectric and piezomagnetic half-spaces with magneto-electro-mechanical imperfect interface

Abstract We study the propagation of shear horizontal waves between the interface of piezoelectric and piezomagnetic half-spaces with a magneto-electro-mechanical imperfect contact. Mechanical, electrical and magnetical imperfections are modelled by means of a spring, a capacitor and a inductor, respectively. A general expression for the dispersion relation not reported previously in literature is given in an explicit form, with the diverse limit cases analysed in detail. In some of these limit cases, new expressions are also obtained which predict the existence of interfacial waves. In the other cases, when already reported results exist, a comparison with them is done. Some physical interpretations are derived from the limit cases. The influence of mechanical, electrical and magnetical imperfect contacts are shown in some numerical examples.

Asymptotic Study on a Soft Thin Layer: The Non-Convex Case

It is proposed to model the adhesive bonding of elastic bodies when the adhesive is a phase-transforming material. For this purpose, the (isothermal) Frémond model is adopted, including only two variants of martensite. In the first part of this paper, asymptotic expansions are used to study the asymptotic behavior of the adhesive as its thickness and elastic coefficients tend toward zero. In the second part, the energy minimization approach is used and the equilibrium of a one-dimensional bar is studied in detail. The simplified one-dimensional context adopted here makes it possible to compute contact laws taking nucleation and the kinetics of the phase transformation explicitly into account.

An Interface Model Including Cracks and Roughness Applied to Masonry

In this paper an interface model accounting for roughness and micro-cracks is presented and applied to masonry-like structures. The model is consistently derived by coupling a homogenization approach and arguments of asymptotic analyses. A numerical procedure is introduced and numerical results, based on a finite element formulation, are successfully compared with experimental data , obtained on masonry samples undergoing to shear tests. Finally, a parametric numerical analysis is proposed, highlighting the influence of the roughness features on the interface response.

Characterization of piezoelectric composites with mechanical and electrical imperfect contacts

The aim of the present work is to study the influence of the mechanical and electrical imperfections in reinforced piezoelectric composite materials with unidirectional cylindrical fibers periodically distributed in rhombic cells under mechanical and electrical imperfect contacts. The behavior of the composites is studied through two approaches: the two-scale asymptotic homogenization method and the finite element method. The asymptotic homogenization method is applied to a two-phase composite with mechanical and electrical imperfect contacts and to a three-phase composite with perfect contact in the interphase. The constituents of the composite are homogeneous piezoelectric materials with transversely isotropic properties. The local problems are formulated for the spring-capacitor and three-phase models by the asymptotic homogenization method. The solution of each plane local problem is found using potential methods of a complex variable and the properties of doubly periodic Weierstrass elliptic functions. Closed-form formulae are obtained for the effective properties of the composites with both types of imperfect contacts and different configuration of the cells. The finite element method is implemented for analysis of piezoelectric composite materials with unidirectional cylindrical fibers periodically distributed in rhombic cells under mechanical and electrical imperfect contacts. Some numerical examples are given under the presence of both imperfect contacts and different arrangement of the cells. Comparisons between the numerical results reported by asymptotic homogenization method and finite element method are provided.

Process parameters influence on mechanical strength of direct bonded surfaces for both materials: Silica and Zerodur glasses

Direct bonding is of particular interest for optical system manufacturing for spatial application. This technology is already used in terrestrial optical system manufacturing because of the very high precision of the process and complex geometries are able to bond. However, even if a first prototype already passed with success space environment test, quantification and improvement of the mechanical strength of assemblies are essential to validate the assembly’s life expectancy and to validate the European Space Agency standards. So, this work proposes to study the influence of process parameters, such as roughness, relative air humidity during room temperature bonding, annealing time and temperature, on mechanical strength of an elementary mechanical structure using a double shear test procedure and cleavage tests. At the same time, the performances of fused silica and Zerodur® glasses are compared. For the process considered in this study, a parallel is made between chemical phenomena, surface roughness and mechanical strength. In the end, cleavage tests confirm the choice of the optimal process parameters and highlight a damaging phenomenon of bonded interfaces with successive re-adhesion.

Multiscale Modeling of Imperfect Interfaces and Applications

Modeling interfaces between solids is of great importance in the fields of mechanical and civil engineering. Solid/solid interface behavior at the microscale has a strong influence on the strength of structures at the macroscale, such as gluing, optical systems, aircraft tires, pavement layers and masonry, for instance. In this lecture, a deductive approach is used to derive interface models, i.e. the thickness of the interface is considered as a small parameter and asymptotic techniques are introduced. A family of imperfect interface models is presented taking into account cracks at microscale. The proposed models combine homogenization techniques for microcracked media both in three-dimensional and two-dimensional cases, which leads to a cracked orthotropic material, and matched asymptotic method. In particular, it is shown that the Kachanov type theory leads to soft interface models and, alternatively, that Goidescu et al. theory leads to stiff interface models. A fully nonlinear variant of the model is also proposed, derived from the St. Venant-Kirchhoff constitutive equations. Some applications to elementary masonry structures are presented.

Thermomechanical analysis of an aircraft tire in cornering using coupled ale and lagrangian formulations

The thermomechanical behavior of an aircraft tire is predicted, using experimental devices, a model based on finite element software and an appropriate method of expressing the heat generated by skid in terms of the local friction coefficient, depending on the temperature. In the thermomechanical model, a steady state mechanical analysis is combined with a transient thermal problem. This combined approach is based on three main computing steps: the deformation step, the dissipation step and the thermal step. The deformation step calculates the stress and the velocity fields, which are used as inputs in the dissipation step to calculate the heat generated due to friction. The internal dissipation is assumed to be negligible. Finally, the thermal step yields new thermal maps based on the heat flux computed in the dissipation step. The coupling is established by updating the friction coefficient in the first two steps.

Thermomechanical Couplings in Aircraft Tire Rolling/Sliding Modeling

This paper presents a finite element model for the simulation of aircraft tire rolling. Large deformations, material incompressibility, heterogeneities of the material, unilateral contact with Coulomb friction law are taken into account. The numerical model will allow estimating the forces in the contact patch - even in critical and extreme conditions for the aircraft safety and security. We show the influence of loading parameters (vertical load, velocity, inflating pressure) and slip angle on the Self Aligning torque and on the lateral friction coefficient. A friction coefficient law corresponding to Chichinadze model is considered to take into account thermal effects in the aircraft tire model behaviour.

Assessment of models and methods for pressurized spherical composites

The elastic properties of a spherical heterogeneous structure with isotropic periodic components is analyzed and a methodology is developed using the two-scale asymptotic homogenization method (AHM) and spherical assemblage model (SAM). The effective coefficients are obtained via AHM for two different composites: (a) composite with perfect contact between two layers distributed periodically along the radial axis; and (b) considering a thin elastic interphase between the layers (intermediate layer) distributed periodically along the radial axis under perfect contact. As a result, the derived overall properties via AHM for homogeneous spherical structure have transversely isotropic behavior. Consequently, the homogenized problem is solved. Using SAM, the analytical exact solutions for appropriate boundary value problems are provided for different number of layers for the cases (a) and (b) in the spherical composite. The numerical results for the displacements, radial and circumferential stresses for both methods are compared considering a spherical composite material loaded by an inside pressure with the two cases of contact conditions between the layers (a) and (b).

On modelling brick/mortar interface via a St. Venant-Kirchhoff orthotropic soft interface. Part II: in silico analysis

A new strategy for the numerical modelling of brick/mortar interfaces at the macro-scale taking into account finite strains and evolving microcracking phenomena is introduced. A numerical validation of the non-linear-imperfect interface model formulated in Part I of the present paper, is proposed. Well-established experimental data concerning diagonal compression of masonry walls are simulated within the finite element method. The localisation zones of highest displacement jumps and stresses obtained through the numerical simulations are in good agreement with the experimental findings. The proposed non-linear interface model is also compared with a linear interface model for masonry structures.