In timber-concrete composite systems, timber and concrete are inherently brittle materials that behave linearly elastic in both tension and bending. However, the shear connection between the members can exhibit significant ductility. It is therefore possible to develop timber-concrete composite systems with ductile connection that behave in a ductile fashion. This study illustrates the use of an elastic-perfectly plastic analytical approach to this problem. In addition, the study proposes an incremental method for predicting the nonlinear load-deflection response of the composite system. The accuracy of the analytical model is confirmed with a computer model, and numerical solutions of the analytical model are compared to experimental results from the bending tests conducted by previous researchers. Reasonable agreement is found from the comparisons, which validates the capacity of the analytical model in predicting the structural behaviour of the timber-concrete composite systems in both elastic and post-elastic stages.

In timber-concrete composite systems, timber and concrete are inherently brittle materials that behave linearly elastic in both tension and bending. However, the shear connection between the members can exhibit significant ductility. It is therefore possible to develop timber-concrete composite systems with ductile connection that behave in a ductile fashion. This study illustrates the use of an elastic-perfectly plastic analytical approach to this problem. In addition, the study proposes an incremental method for predicting the nonlinear load-deflection response of the composite system. The accuracy of the analytical model is confirmed with a computer model, and numerical solutions of the analytical model are compared to experimental results from the bending tests conducted by previous researchers. Reasonable agreement is found from the comparisons, which validates the capacity of the analytical model in predicting the structural behaviour of the timber-concrete composite systems in both elastic and post-elastic stages.

Ce travail porte sur le développement de méthodes d'homogénéisation numériques pour les matériaux non linéaires élastoplastiques et élasto-visco plastiques avec pour finalité le calcul de structures hétérogènes faite de ces matériaux sous chargements cycliques. Les techniques proposées se basent sur des approches incrémentales. Dans une première partie, nous développons une méthodologie pour déterminer la taille du VER dans le cas non linéaire pour les types de comportements cités précédemment. Pour cela, une étude de la convergence statistique de paramètres d'une loi semi-analytique incrémentale est menée. Cette méthode permet de diminuer les temps de calcul pour l'identification des paramètres et ainsi qu'une meilleure approximation de la loi de comportement effective, qui peut ensuite être utilisée dans un calcul de structure. Dans une deuxième partie, nous proposons une méthode d'homogénéisation numérique incrémentale dans laquelle l'originalité est de calculer le module tangent effectif par superposition de solutions numériques calculées par éléments finis sur le VER, en exploitant la linéarisation du problème à caque incrément. Un schéma alternatif aux techniques telles que la méthode Eléments finis multi niveaux (FE2) est ainsi développé, avec pour avantage un nombre réduit de calculs éléments finis à effectuer sur le VER. La technique est appliquée au calcul de structures hétérogènes non linéaires élastoplastiques, pour des microstructures anisotropes ou de morphologies complexes, et pour des lois de comportement locales élastoplastiques avec écrouissage isotrope et cinématique / In this work, computational homogenization methods for nonlinear materials with elasto-plastic and elasto-visco-plastic phases are developed, with application to the computation of heterogeneous structures made of these nonlinear materials under cyclic loading. The proposed techniques are based on incremental approaches. In a first part, we develop a methodology to determine the size of an RVE in the nonlinear case for the types of nonlinear behavior mentioned above. For this purpose, a convergence study of the parameters of a semi-analytical incremental constitutive law is carried out. This method allows reducing computational times related to the identification of these parameters and provides a better approximation of the effective constitutive relationship, which can then be used in a structure calculation once identified. In a second part, we propose an incremental computatioal homogenization method in which the originality is to compute directly the effective tangent tensor by superposition of numerical solutions computed by finite elements on an RVE, by taking advantage of the linearization of the problem at each increment. An alternative scheme to classical multilevel finite element techniques (FE2) is then developed, with the advantage of a reduced number of computations to perform on the RVE. The technique is applied to the computation of heterogeneous, nonlinear structures, for anisotropic microstructures or with complex morphologies and for phase with elastoplastic behavior with isotropic and kinematic hardening

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