Predicting the mechanical behavior of two-phase materials with cellular automata

A new mechanical model is proposed to predict the mechanical behavior of inhomogeneous materials. The simple case of an aggregate of two linearly viscous phases submitted to plane strain is addressed here. Calculations involve the Eshelby localization relationships associated with a Walpole-type averaging procedure. When the grains are equiaxed, derivations are entirely analytical, which allows the proposed method to be simply compared with the classical Hashin-Shtrikman lower and upper bounds and the self-consistent model. When large strains are considered, the model is used to predict numerically the overall stress-strain relationships. Significant morphological hardening or softening is shown to occur with increasing strain, depending on the initially equiaxed or elongated grain shapes. Finally, the local distributions of strains, and thus the development of strain inhomogeneities, are also predicted by the model.