Some elements of microstructural mechanics

Microstructural mechanics combines the computational methods of structural mechanics and materials sciences. It is dedicated to the mechanics of heterogeneous materials. On the one hand, it can be used to compute industrial components for which the size of the heterogenities is of the order of magnitude of the size of the structure itself or of holes or notches. On the other hand, the computation of representative volume elements of heterogeneous materials enables one to predict the influence of phase morphology and distribution on the linear or non-linear effective properties, having in view microstructure optimization. Such computations provide the local stress–strain fields that can be used to predict damage or crack initiation. This work focuses on the modern tools available for reconstructing realistic three-dimensional microstructures and for computing them, including parallel computing. The choice of the local non-linear constitutive equations and the difficulty of identification of the corresponding parameters remain the weakest link in the methodology. The main example detailed in this work deals with polycrystalline plasticity and illustrates the tremendous heterogeneity of local stress and strain, and the effect of grain boundary or free surfaces. The computations are finally used to calibrate a simplified homogenization polycrystal model.