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International audience; Contact problems are very important in the engineering design and the correct interpretation of the physical phenomena, and its influence in this process, is of paramount importance for the engineers. In this paper we employ the topological derivative concept for optimum design problems in contact solid mechanics. A nonlinear contact model governed by a variational inequality is considered. Beside the theoretical developments, some computational examples are included. The influence of the parameters of the contact model in the optimal results for the structures is studied. The numerical results show that the proposed method of optimum design can be applied to a broad class of engineering problems.

In the paper the general method for shape-topology sensitivity analysis of contact problems is proposed. The method uses the domain decomposition method combined with the specific properties of minimizers for the energy functional. The method is applied to the static problem of an elastic body in frictionless contact with an rigid foundation. The contact model allows a finite interpenetration of the bodies on the contact region. This interpenetration is modeled by means of a scalar function that depends on the normal component of the displacement field on the potential contact zone. We present the asymptotic behavior of the energy shape functional when a spheroidal void is introduced in an arbitrary point of the elastic body. For the asymptotic analysis, we use the domain decomposition technique and the associated Steklov-Poincaré pseudodifferential operator. The differentiability of the energy with respect to the non-smooth perturbation is established. A closed form for the topological derivative is also presented.

A recently proposed algorithm for micro-structural optimization, based on the concept of topological derivative and a level-set domain representation, is applied to the synthesis of elastic and heat conducting bi-material micro-structures. The macroscopic properties are estimated by means of a family of multi-scale constitutive theories where the macroscopic strain and stress tensors (temperature gradient and heat flux vector in the heat conducting case) are defined as volume averages of their microscopic counterparts over a Representative Volume Element (RVE). Several finite element-based examples of micro-structural optimization are presented. Three multi-scale models, providing an upper and a lower bound for the macroscopic properties as well as the classical periodic medium solution, are considered in the optimization process. These models differ only in the kinematical constraints (thermal constraints in the heat conducting case) imposed on the RVE. The examples show that, in general, the obtained optimum micro-structure topology depends on the particular model adopted. Fil: De Souza Neto, Eduardo Alberto. Swansea University; Reino Unido Fil: Amstutz, Samuel. No especifíca; Fil: Giusti, Sebastian Miguel. Laboratório Nacional de Computação Científica; Brasil. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba; Argentina Fil: Novotny, Antonio André. Laboratório Nacional de Computação Científica; Brasil

This book brings together some 20 chapters on state-of-the-art research in the broad field of computational plasticity with applications in civil and mechanical engineering, metal forming processes, geomechanics, nonlinear structural analysis, composites, biomechanics and multi-scale analysis of materials, among others. The chapters are written by world leaders in the different fields of computational plasticity.