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In the first part of this contribution, a brief theoretical revision of the mechanical and variational foundations of a Failure-Oriented Multiscale Formulation devised for modeling failure in heterogeneous materials is described. The proposed model considers two well separated physical length scales, namely: (i) the macroscale where nucleation and evolution of a cohesive surface is considered as a medium to characterize the degradation phenomenon occurring at the lower length scale, and (ii) the microscale where some mechanical processes that lead to the material failure are taking place, such as strain localization, damage, shear band formation, and so on. These processes are modeled using the concept of Representative Volume Element (RVE). On the macroscale, the traction separation response, characterizing the mechanical behavior of the cohesive interface, is a result of the failure processes simulated in the microscale. The traction separation response is obtained by a particular homogenization technique applied on specific RVE sub-domains. Standard, as well as, Non-Standard boundary conditions are consistently derived in order to preserve objectivity of the homogenized response with respect to the micro-cell size. In the second part of the paper, and as an original contribution, the detailed numerical implementation of the two-scale model based on the finite element method is presented. Special attention is devoted to the topics, which are distinctive of the Failure-Oriented Multiscale Formulation, such as: (i) the finite element technologies adopted in each scale along with their corresponding algorithmic expressions, (ii) the generalized treatment given to the kinematical boundary conditions in the RVE, and (iii) how these kinematical restrictions affect the capturing of macroscopic material instability modes and the posterior evolution of failure at the RVE level. Finally, a set of numerical simulations is performed in order to show the potentialities of the proposed methodology, as well as, to compare and validate the numerical solutions furnished by the two-scale model with respect to a direct numerical simulation approach. Fil: Toro, Sebastian. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Centro de Investigaciones en Métodos Computacionales. Universidad Nacional del Litoral. Centro de Investigaciones en Métodos Computacionales; Argentina Fil: Sánchez, Pablo Javier. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Centro de Investigaciones en Métodos Computacionales. Universidad Nacional del Litoral. Centro de Investigaciones en Métodos Computacionales; Argentina Fil: Huespe, Alfredo Edmundo. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Centro de Investigaciones en Métodos Computacionales. Universidad Nacional del Litoral. Centro de Investigaciones en Métodos Computacionales; Argentina Fil: Giusti, Sebastian Miguel. Universidad Tecnológica Nacional. Facultad Regional Córdoba; Argentina Fil: Blanco, Pablo Antonio. Laboratorio Nacional de Computacao Cientifica; Brasil Fil: Feijóo, Raúl Antonino. Laboratorio Nacional de Computacao Cientifica; Brasil

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.

Submitted by Maria Cristina (library@lncc.br) on 2015-11-25T12:00:01Z No. of bitstreams: 1 Tese - Análise de Sensibilidade Topológica.pdf: 447139 bytes, checksum: d7d9c80ad59acb3e3cf12ae2d457887f (MD5) Approved for entry into archive by Maria Cristina (library@lncc.br) on 2015-11-25T12:00:22Z (GMT) No. of bitstreams: 1 Tese - Análise de Sensibilidade Topológica.pdf: 447139 bytes, checksum: d7d9c80ad59acb3e3cf12ae2d457887f (MD5) Made available in DSpace on 2015-11-25T12:00:35Z (GMT). No. of bitstreams: 1 Tese - Análise de Sensibilidade Topológica.pdf: 447139 bytes, checksum: d7d9c80ad59acb3e3cf12ae2d457887f (MD5) Previous issue date: 2015-11-03 Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (Capes) The topological derivative concept has been proved to be useful in many relevant applications such as topology optimization, inverse problems, image processing, multi-scale constitutive modeling, fracture mechanics and damage evolution modeling. The topological asymptotic analysis has been fully developed for a wide range of problems modeled by partial di erential equations. On the other hand, the topological derivatives associated with coupled problems have been derived only in their abstract forms. In this paper, therefore, we deal with the Reissner-Mindlin plate bending model, which is written in the form of a coupled system of partial di erential equations. In particular, the topological asymptotic analysis of the associated total potential energy is developed and the topological derivative with respect to the nucleation of a circular inclusion is derived in its closed form.Finally, we provide the estimates for the remainders of the topological asymptotic expansion and perform a complete mathematical justi cation for the derived formulas. O conceito de derivada topológica tem se mostrado útil em muitas aplicações, tais como otimização topológica, problemas inversos, processamento de imagens, modelagem constitutiva multi-escala, mecânica da fratura e modelagem da evolução de dano. A análise assintótica topológica foi amplamente desenvolvida para uma grande variedade de problemas modelados por equações diferenciais parciais. Por outro lado, a derivada topológica associada a problemas acoplados é conhecida apenas em sua forma abstrata. Neste trabalho, portanto, considera-se o modelo de flexão de placa de Reissner-Mindlin, que é escrito na forma de um sistema acoplado de equações diferenciais parciais. Em particular, a análise assintótica topológica da energia potencial total associada é desenvolvida e a derivada topológica com relação a nucleação de uma inclusão circular é obtida na sua forma fechada. Finalmente, os resíduos da expansão assintótica topológica são estimados e uma justificativa matemática completa para a derivada topológica é apresentada.