Determinar o comportamento de materiais reforçados a partir do conhecimento das propriedades individuais de seus componentes é assunto de uma quantidade considerável de pesquisas experimentais e teóricas nas últimas décadas. Nesse trabalho, um modelo multifásico para determinação do comportamento macroscópico de estruturas de concreto armado no contexto da elastoplasticidade e considerando a interação entre o concreto e as armaduras é apresentado e incorporado em um código numérico em elementos finitos. Em uma escala macroscópica o meio multifásico é tomado como a superposição geométrica de meios contínuos em interação mútua, chamados de fase matriz e fase reforço. Cada fase possui cinemáticas distintas oferecendo, desta forma, um arcabouço adequado para levar em conta o deslizamento das barras de aço em relação à matriz de concreto. As equações de movimento são desenvolvidas com a aplicação do método dos trabalhos virtuais. A evolução elastoplástica é obtida a partir da avaliação de um critério próprio para cada constituinte e para interação, computando as tensões parciais correspondentes e obtendo um comportamento desacoplado por fase. A resistência do concreto em um estado de tensões multiaxial é estimada a partir do critério de falha de Ottosen e a fissuração do concreto é representada utilizando um modelo de fissuras distribuídas. Utilizando uma implementação tridimensional em elementos finitos, a ferramenta numérica desenvolvida é aplicada para analisar vigas e lajes sob carregamento prescrito e uma boa concordância entre os resultados numéricos e experimentais é obtida. Ao final é apresentado uma análise de ensaio de arrancamento onde o principal objetivo é a investigação dos parâmetros relevantes que controlam a lei de interação entre o concreto e as barras de aço. / Predicting the behavior of reinforced materials from the knowledge of the individual properties of its components has been a subject of several experimental and theoretical works in recent years. In this work, a multiphase model for assessing the macroscopic behavior of reinforced concrete structures in the context of elastoplasticity and accounting for the interaction between the reinforcing bars and the surrounding concrete is presented and implemented in a finite element numerical code. Considering a macroscopic scale, the multiphase model is regarded as superposition of several continua in mutual interaction, namely matrix phase and reinforcement phase. For each phase different kinematics are attributed providing a suitable framework to consider the slippage between the matrix and the reinforcement. The general equations of motion are derived by means of the virtual work method. The elastoplastic evolution is carried out considering each phase and the interaction separately, computing the corresponding partial stresses and projecting onto the yield domain of the multiphase medium. The strength of concrete under multiaxial states of stress is estimated from the so-called Ottosen failure criterion and the concrete cracking issue is accounted with a smeared crack model. Using a three-dimensional finite element implementation, the numerical tool developed is applied to analyze reinforced concrete beams and slabs under prescribed loading and a good agreement between numerical and experimental results is obtained. Finally, the investigation of the main parameters that govern the interaction law of concrete and reinforcing bars has been the central purpose of the pullout tests simulations.

Orientador: Philippe Remy Bernard Devloo / Dissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Engenharia Civil, Arquitetura e Urbanismo / Made available in DSpace on 2018-08-18T01:44:23Z (GMT). No. of bitstreams: 1 Cecilio_DiogoLira_M.pdf: 5163879 bytes, checksum: 102fa941f977c8a36107d3d37f05c5af (MD5) Previous issue date: 2011 / Resumo: Este estudo revisa os fundamentos da teoria da plasticidade incremental em uma formulação elastoplástica do comportamento no ponto material e sua ligação com o método dos elementos finitos. Documenta a implementação na linguagem de programação C++ dos modelos elastoplásticos de Drucker-Prager, Mohr-Coulomb e von Mises. É realizado uma série de simulações de carregamento uniaxial para os modelos implementados e finalmente solucionados três problemas elastoplásticos em elementos finitos. Em cada um dos problemas resolvidos foi utilizado o modelo elastoplástico adequado ao material do problema em questão. Os problemas solucionados foram todos em estado plano de deformação e consistiram em: i) um ensaio de compressão diametral; ii) um problema de estabilidade de taludes; iii) e um tubo de aço pressurizado internamente. A implementação da formulação elastoplástica foi validada comparando os resultados das simulações com os da literatura / Abstract: This work reviews the fundamentals of the theory of plasticity in an incremental formulation of the elastoplastic behavior at a material point and its connection with the finite element method. It documents the implementation of the elastoplastic models of Drucker-Prager, Mohr-Coulomb and von Mises in the programming language C++. A series of simulations of uniaxial loading models are carried out and three problems in elastoplastic finite element method are solved. In each of the modeled cases the most appropriate elastoplastic model among those implemented is employed. The problems were solved in plane strain state and comprise: i) a diametral compression test of concrete or Brazilian Disc Test; ii) a problem of slope stability; iii) and an internally pressurized vessel. The implementation of the elastoplastic formulation was validated by comparing the simulation results with the results from the literature / Mestrado / Estruturas / Mestre em Engenharia Civil

Orientador: Philippe Remy Bernard Devloo / Tese (doutorado) - Universidade Estadual de Campinas, Faculdade de Engenharia Civil, Arquitetura e Urbanismo / Made available in DSpace on 2018-08-14T23:57:56Z (GMT). No. of bitstreams: 1 Santos_ErickSlisRaggio_D.pdf: 9701048 bytes, checksum: ef950a7408bf4167850acdaf6ee45a45 (MD5) Previous issue date: 2009 / Resumo: A exploração de recursos minerais tem se apresentado como uma atividade de destaque na economia brasileira. Os ambientes nos quais estes recursos são encontrados se apresentam complexos e desafiadores à produção e requerem tecnologia e conhecimento indisponíveis no mercado para permitir converter reservas em produção. No âmbito da perfuração e completa ção de poços de petróleo, torna-se cada vez mais importante a compreensão e reprodução do comportamento hidromecânico de rochas em profundidade. É comum o emprego da teoria da elastoplasticidade para a modelagem dos comportamentos de deformações reversíveis e irreversíveis observados em rochas. A modelagem do comportamento hidráulico do meio poroso conduz a acoplamentos poroelastoplásticos de diversas naturezas. Contudo, não foi encontrado na literatura um texto único que postule a formulação poroelastoplástica considerando a contrapartida plástica do armazenamento de fuidos na formação. Neste trabalho objetiva-se reunir uma formulação poroelastoplástica consistente capaz de empregar modelagens constitutivas elastoplásticas que reproduzem mais fidedignamente o comportamento de rochas em relação aos largamente empregados modelos baseados na superfície de falha de Mohr-Coulomb. São empregados os modelos constitutivos de Lade-Kim e Sandler e Dimaggio, que apresentam endurecimento isotrópico e são capazes de modelar comportamentos de compactação e controle de dilatância. Formula-se também um algoritmo genérico de decomposição elastoplástica com controle de erro por subincrementação e capaz de determinar a matriz tangente elastoplástica consistente com auxílio de estratégias de diferenciação automática. A implementação deste módulo na linguagem C++ genérica e orientada a objetos, juntamente com módulos de análise elastoplástica e poroelastoplástica, permitiram a extensão do ambiente de computação científica PZ para modelar estes tipos de problemas. Como resultado obtiveram-se algoritmos bastante robustos e respostas mecânica e hidromecânica de simulações de perfuração de poços bastante condizentes com a experiência do doutorando. / Abstract: The exploration of mineral resources is growing in importance in the Brazilian economy. Since the environments in which these resources are found are becoming increasingly more complex and challenging for the production phase, currently unavailable knowledge and technologies are required to produce these reserves. In the particular well drilling and completion areas, the comprehension and numerical reproduction of the hydromechanical behavior of rocks in such deep environments become an issue. The observed reversible and irreversible strain behavior of rocks is commonly modeled by the elastoplasticity theory. The hydraulic modeling of a porous media leads to poroelastoplastic couplings of several kinds, but an unique text on poroelastoplastic postulation concerning the plastic counterpart of fluid storage in the formation had not been found in the bibliography. Thus, this thesis aims for the development of a consistent poroelastoplastic formulation applied to the elastoplastic consitutive models of Lade-Kim and Sandler & Dimaggio. These models embody isotropic hardening and allow the correct modeling of rock compaction and controled dilatancy, resembling the rock behavior in a more reliable sense than the conventional and largerly applied models based on the Mohr-Coulomb yield surface. The author presents a generic elastoplastic decomposition algorithm with adaptive substepping in order to constrain the ODE's integration deviation. A consistent jacobian operator evaluation becomes feasible by the adoption of automatic differentiation strategies. The final C++ implemented generic and object-oriented elastoplastic decomposition and elastoplastic and poroelastoplastic simulation modules extend the PZ scientific computation environment to the simulation of such problems. The resultant algorithms presented high computational robustness and mechanical and hydromechanical well drilling behavior agreeing to the author's experience. / Doutorado / Estruturas / Doutor em Engenharia Civil

Orientador: Philippe Remy Bernard Devloo / Tese (doutorado) - Universidade Estadual de Campinas, Faculdade de Engenharia Mecânica e Instituto de Geociências / Made available in DSpace on 2018-08-26T09:47:31Z (GMT). No. of bitstreams: 1 Cecilio_DiogoLira_D.pdf: 15685431 bytes, checksum: 55d69e06f21da53c6ad09132dfbf4337 (MD5) Previous issue date: 2014 / Resumo: No presente trabalho é construído um código eficiente para a simulação do comportamento mecânico de um poço de petróleo na fase de perfuração, com base na discretização de um modelo matemático geral para pequenas deformações elastoplásticas pelo método de Elementos Finitos. A metodologia de cálculo elastoplástico conhecida por projeção sobre o ponto mais próximo da superfície plástica é aplicada ao modelo de Sandler-DiMaggio, o que permite abordar o problema elastoplástico de modelos complexos de forma mais simples e eficiente. Os resultados da resposta material são comparados aos apresentados no artigo original sobre esse modelo. Uma análise de estabilidade de poço utilizando o método dos elementos finitos, juntamente com o modelo elastoplástico proposto, é realizada posteriormente. O comportamento plástico na região em torno do poço é obtido por uma transferência gradual do estado de tensão na parede do mesmo. Para aprimorar a precisão da simulação elastoplástica de Elementos Finitos, aplica-se refinamento e aumento da ordem polinomial aos elementos localizados na região de plastificação. Utiliza-se o segundo invariante do tensor de deformação plástico deviatórico como critério para indicar o colapso do material. Simulações adaptativas requerem a comunicação de informação de uma malha para outra. Sendo assim, um procedimento específico de transferência do histórico de deformação elastoplástica foi criado. A matriz tangente referente ao cálculo da variação da tensão em função da variação da deformação é calculada consistentemente. O modelo numérico elastoplástico é implementado em um contexto de programação orientada a objetos. Ele é aplicado em uma configuração típica de um reservatório carbonático. Observa-se que a mudança de geometria do poço devido ao breakout gera um aumento na magnitude da defomação plástica em uma área progressivamente menor / Abstract: In this work an efficient code for the simulation of the mechanical behavior of an oil well during the drilling phase is constructed. It is based on the discretization of a general mathematical elastoplastic model for small deformations using the Finite Element method. The methodology of the elastoplastic calculation, known as the closest point projection, is applied to the Sandler-DiMaggio modal, which enables addressing the elastoplastic problem of complex models more easily and efficiently. The results of the response is compared to the material presented in the original article about this model. A stability analysis of a well using the Finite Element method with the proposed elastoplastic constitutive modal is then performed. The plastic behaviour in the area around the wellbore is obtained by a gradual transfer of stress state to it. To improve the accuracy of the elastoplastic Finite Element simulation, adaptive refinement and increasing the polynomial order are applied to elements located in the plastification area. The second invariant of the plastic deviatoric strain tensor is used as a damage criterion to indicate the failure of the material. Adaptive simulations require the comunication of information from a mesh to another one. Therefore, a specific transfer procedure for elastoplastic deformation history is created. The tangent matrix related to the stress variation with respect to the strain variation is ??calculated consistently. The elastoplastic numerical model is implemented in the context of object-oriented programming. It is applied to a typical configuration of a carbonate reservoir. It is observed that the change in geometry due to the well breakout generates an increase in the magnitude of plastic defomação in a progressively smaller area / Doutorado / Explotação / Doutor em Ciências e Engenharia de Petróleo

Doctor of Philosophy / Department of Mechanical and Nuclear Engineering / Prakash Krishnaswami / Xiao J. Xin / Over the past two decades meshless methods have attracted much attention owing to their advantages in adaptivity, higher degree of solution field continuity, and capability to handle moving boundary and changing geometry. In this work, a meshless integral method based on the regularized boundary integral equation has been developed and applied to two-dimensional linear elasticity and elastoplasticity with small or large deformation. The development of the meshless integral method and its application to two-dimensional linear elasticity is described first. The governing integral equation is obtained from the weak form of elasticity over a local sub-domain, and the moving least-squares approximation is employed for meshless function approximation. This formulation incorporates: a subtraction method for singularity removal in the boundary integral equation, a special numerical integration for the calculation of integrals with weak singularity which further improves accuracy, a collocation method for the imposition of essential boundary conditions, and a method for incorporation of natural boundary conditions in the system governing equation. Next, elastoplastic material behavior with small deformation is introduced into the meshless integral method. The constitutive law is rate-independent flow theory based on von Mises yielding criterion with isotropic hardening. The method is then extended to large deformation plasticity based on Green-Naghdi’s theory using updated Lagrangian description. The Green-Lagrange strain is decomposed into the elastic and plastic part, and the elastoplastic constitutive law is employed that relates the Green-Lagrange strain to the second Piola-Kirchhoff stress. Finally, a pre- and post-processor for the meshless method using node- and pixel-based approach is presented. Numerical results from the meshless integral method agree well with available analytical solutions or finite element results, and the comparisons demonstrate that the meshless integral method is accurate and robust. This research lays the foundation for modeling and simulation of metal cutting processes.

Orientador: Philippe Remy Bernard Devloo / Dissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Engenharia Civil, Arquitetura e Urbanismo / Made available in DSpace on 2018-08-26T15:50:44Z (GMT). No. of bitstreams: 1 Shauer_Nathan_M.pdf: 4772079 bytes, checksum: c339b53fa640108ef53c5f66523a128c (MD5) Previous issue date: 2015 / Resumo: Fraturamento Hidráulico é o processo pelo qual uma fratura se propaga através da injeção de um fluido pressurizado em seu interior. É muito utilizado na indústria de petróleo, pois cria uma zona de alta condutividade, possibilitando aumento nas taxas de injeção ou produção. Esse trabalho consiste na implementação numérica, no ambiente orientado a objetos NeoPZ, de uma fratura propagando hidraulicamente em um domínio bidimensional pelo método dos elementos finitos. Os fenômenos envolvidos considerados são a resposta mecânica do reservatório utilizando a relação tensão deformação elastoplástica, junto com escoamento entre placas planas no interior da fratura, incluindo o efeito de leak-off dado pelo modelo de Carter. Os critérios de plastificação utilizados são o de Mohr-Coulomb, que é usado para comparar os resultados com os de Papanastasiou, P. [1], e o de Sandler-DiMaggio, que é referenciado por Santos, E. S. [2] como sendo um bom critério para modelar a relação constitutiva de formações de óleo e gás. São utilizados conceitos de c++ orientação a objetos, materiais coesivos para critério de propagação, acoplamento completo de fenômenos e utilização de espaços reduzidos. As rotinas implementadas são verificadas de acordo com equações analíticas e observando que a conservação de massa é satisfeita. Com esse estudo confrontam-se os resultados obtidos pela abordagem da Elasticidade Linear usualmente utilizada, percebendo que a simulação de fraturamento hidráulico com elastoplasticidade, devido a plastificação da ponta, gera fraturas com menores comprimentos e maiores aberturas para um mesmo volume de injeção como observado por Papanastasiou, P. et al. [1, 3, 4] / Abstract: Hydraulic Fracturing is the process in which a fracture propagates through the injection of a pressurized fluid in its interior. It is widely used in the oil industry due to the high conductivity zone it creates, which provides high rates of both injection and production. This work consists in the numerical implementation, in the object oriented environment NeoPZ, of a fracture hydraulically propagating in a two dimensional elastoplastic medium using the Finite Elements method. The involved phenomena considered are the mechanical response of the reservoir, using the elastoplastic stress-strain relationship, along with the flow between plane plates within the fracture and considering the leak-off on the walls of the fracture using the Carter model. The elastoplastic criteria used are the Mohr-Coulomb criteria, which is used to compare results with the ones from Papanastasiou, P. [1], and the Sandler-DiMaggio criteria, which is referenced by Santos, E. S. [2] as a good criteria to model the constitutive relation of oil and gas formations. Some of the concepts used in this work are c++ object oriented language, cohesive zone for fracture propagation, fully coupling of the involved phenomena, and use of reduced spaces. The routines implemented in this work are verified according to analytical equations and verifying that the conservation law is satisfied. In this study the results obtained are compared with the Linear Elasticity approach, which is commonly used, realizing that simulation of hydraulic fracturing using elastoplastic constitutive laws, due to the yielding of the tip, generates smaller fracture lengths and larger apertures for the same injection volume as observed by Papanastasiou, P. et al. [1, 3, 4] / Mestrado / Estruturas e Geotécnica / Mestre em Engenharia Civil

Recent advances in machine learning have unlocked new potential for innovation in engineering science. Neural networks are used as universal function approximators that harness high-dimensional data with excellent learning capacity. While this is an opportunity to accelerate computational mechanics research, application in constitutive modeling is not trivial. Machine learning material response predictions without enforcing physical constraints may lack interpretability and could be detrimental to high-risk engineering applications. This dissertation presents a meta-modeling framework for automating the discovery of elastoplasticity models across material scales with emphasis on establishing interpretable and, hence, trustworthy machine learning modeling tools. Our objective is to introduce a workflow that leverages computational mechanics domain expertise to enforce / post hoc validate physical properties of the data-driven constitutive laws. Firstly, we introduce a deep learning framework designed to train and validate neural networks to predict the hyperelastic response of materials. We adopt the Sobolev training method and adapt it for mechanics modeling to gain control over the higher-order derivatives of the learned functions. We generate machine learning models that are thermodynamically consistent, interpretable, and demonstrate enhanced learning capacity. The Sobolev training framework is shown through numerical experiments on different material data sets (e.g. β-HMX crystal, polycrystals, soil) to generate hyperelastic energy functionals that predict the elastic energy, stress, and stiffness measures more accurately than the classical training methods that minimize L2 norms. To model path-dependent phenomena, we depart from the common approach to lump the elastic and plastic response into one black-box neural network prediction. We decompose the elastoplastic behavior into its interpretable theoretical components by training separately a stored elastic energy function, a yield surface, and a plastic flow that evolve based on a set of deep neural network predictions. We interpret the yield function as a level set and control its evolutionas the neural network approximated solutions of a Hamilton-Jacobi equation that governs the hardening/softening mechanism. Our framework may recover any classical literature yield functions and hardening rules as well as discover new mechanisms that are either unbeknownst or difficult to express with mathematical expressions. Through numerical experiments on a 3D FFT-generated polycrystal material response database, we demonstrate that our novel approach provides more robust and accurate forward predictions of cyclic stress paths than black-box deep neural network models. We demonstrate the framework's capacity to readily extend to more complex plasticity phenomena, such as pressure sensitivity, rate-dependence, and anisotropy. Finally, we integrate geometric deep learning and Sobolev training to generate constitutive models for the homogenized responses of anisotropic microstructures (e.g. polycrystals, granular materials). Commonly used hand-crafted homogenized microstructural descriptors (e.g. porosity or the averaged orientation of constitutes) may not adequately capture the topological structures of a material. This is overcome by introducing weighted graphs as new high-dimensional descriptors that represent topological information, such as the connectivity of anisotropic grains in an assemble. Through graph convolutional deep neural networks and graph embedding techniques, our neural networks extract low-dimensional features from the weighted graphs and, subsequently, learn the influence of these low-dimensional features on the resultant stored elastic energy functionals and plasticity models.

No description available.

A Displacement Based Optimization (DBO) approach was applied to truss design problems with material nonlinearities, to explore feasibility and verify efficiency of the approach to solve such problem. Various truss sizing problems with holonomic (path-independent) elastoplastic laws were investigated. This type of material nonlinearity allows us to naturally extend the linear elastic truss sizing in the DBO setting to nonlinear problems. A computer program that uses the commercially available optimizer DOT by VR&D and IMSL Linear Programming solver by Visual Numerics was developed to solve this type of problems. For comparison, we chose an important class of minimum-weight truss design problems, where holonomic linear strain hardening behavior was used. Additional examples of optimum design of trusses with elastic perfectly plastic material response that could be easily solved by Limit Design approach using linear programming were investigated for comparison. All demonstrated examples were tested successfully using the DBO approach. Solutions of comparable examples were consistent with the available results by other methods. Computational effort associated with the DBO approach was minimal for all the examples studied. Optimum solutions of several examples proved that the DBO approach is particularly suited for truss topology design where removal of truss members is essential. / Master of Science

Nous proposons dans cette thèse diverses approches, pour l'amélioration de la modélisation et la simulation multi-échelle du comportement des matériaux composites. La modélisation précise et fiable de la réponse mécanique des matériaux composite demeure un défi majeur. L'objectif de ce travail est de développer des méthodologies simplifiées et basées sur des techniques d'homogénéisation existantes (numériques et analytiques) pour une prédiction efficiente du comportement non-linéaire de ces matériaux. Dans un premier temps un choix à été porté sur les techniques d'homogénéisation par champs moyens pour étudier le comportement élastoplastique et les phénomènes d'endommagement ductile dans les composites. Bien que restrictives, ces techniques demeurent les meilleures en termes de coût de calcul et d'efficacité. Deux méthodes ont été investiguées à cet effet: le Schéma Incrémental Micromécanique (SIM) en modélisation mono-site et le modèle Mori-Tanaka en modélisation multi-site (MTMS). Dans le cas d'étude du comportement élastoplastique, nous avons d'une part montré et validé par la méthode des éléments finis que la technique d'homogénéisation SIM donne un résultat plus précis de la modélisation des composites à fraction volumique élevée que celle de Mori-Tanaka, fréquemment utilisée dans la littérature. D'autre part nous avons étendu le modèle de Mori-Tanaka (M-T) généralement formulé en mono-site à la formulation en multi-site pour l'étude du comportement élastoplastique des composites à microstructure ordonnée. Cette approche montre que la formulation en multi-site produit des résultats concordants avec les solutions éléments finis et expérimentales. Dans la suite de nos travaux, le modèle d'endommagement ductile de Lemaître-Chaboche a été intégré à la modélisation du comportement élastoplastique dans les composites dans une modélisation multi-échelle basée sur le SIM. Cette dernière étude révèle la capacité du modèle SIM à capter les effets d'endommagement dans le matériau. Cependant, la question relative à la perte d'ellipticité n'a pas été abordée. Pour finir nous développons un outil d'homogénéisation numérique basé sur la méthode d'éléments finis multi-échelles (EF2) en 2D et 3D que nous introduisons dans le logiciel conventionnel ABAQUS via sa subroutine UMAT. Cette méthode (EF2) offre de nombreux avantages tels que la prise en compte de la non-linéarité du comportement et de l'évolution de la microstructure soumise à des conditions de chargement complexes. Les cas linéaires et non-linéaires ont été étudiés. L'avantage de cette démarche originale est la possibilité d'utilisation de toutes les ressources fournies par ce logiciel (un panel d'outils d'analyse ainsi qu'une librairie composée de divers comportements mécaniques, thermomécaniques ou électriques etc.) pour l'étude de problèmes multi-physiques. Ce travail a été validé dans le cas linéaire sur un exemple simple de poutre en flexion et comparé à la méthode multi-échelle ANM (Nezamabadi et al. (2009)). Un travail approfondi sera nécessaire ultérieurement avec des applications sur des problèmes non-linaires mettant en évidence la valeur de l'outil ainsi développé / We propose in this thesis several approaches for improving the multiscale modeling and simulation of composites’ behavior. Accurate and reliable modeling of the mechanical response of composite materials remains a major challenge. The objective of this work is to develop simplified methodologies based on existing homogenization techniques (numerical and analytical) for efficient prediction of nonlinear behavior of these materials. First choice has been focused on the Mean-field homogenization methods to study the elasto-plastic behavior and ductile damage phenomena in composites. Although restrictive, these techniques remain the best in terms of computational cost and efficiency. Two methods were investigated for this purpose: the Incremental Scheme Micromechanics (IMS) in One-site modeling and the Mori-Tanaka model in multi-site modeling (MTMS). In the framework of elastoplasticity, we have shown and validated by finite element method that the IMS homogenization results are more accurate, when dealing with high volume fraction composites, than the Mori-Tanaka model, frequently used in the literature. Furthermore, we have extended the Mori-Tanaka's model (MT) generally formulated in One-site to the multi-site formulation for the study of elasto-plastic behavior of composites with ordered microstructure. This approach shows that the multi-site formulation produces consistent results with respect to finite element and experimental solutions. In the continuation of our research, the Lemaître-Chaboche ductile damage model has been included to the study of elasto-plastic behavior in composite through the IMS homogenization. This latest investigation demonstrates the capability of the IMS model to capture damage effects in the material. However, the issue on the loss of ellipticity was not addressed. Finally we develop a numerical homogenization tool based on computational homogenization. This novel numerical tool works with 2D and 3D structure and is fully integrated in the conventional finite element code ABAQUS through its subroutine UMAT. The (FE2) method offers the advantage of being extremely accurate and allows the handling of more complex physics and geometrical nonlinearities. Linear and non-linear cases were studied. In addition, its combination with ABAQUS allows the use of major resources provided by this software (a panel of toolbox for various mechanical, thermomechanical and electrical analysis) for the study of multi-physics problems. This work was validated in the linear case on a two-scale analysis in bending and compared to the multi-scale method ANM (Nezamabadi et al. (2009)). Extensive work will be needed later with applications on non-linear problems to highlight the value of the developed tool