Computational homogenisation approach applied to improve mechanical properties of heterogeneous materials

This article addresses numerical simulation of the mechanical behaviour of materials comprising heterogeneous ductile micro-structures in the presence of voids using a multi-scale approach considering plasticity processes. This kind of material has been used in several applications as structural solutions. Therefore, for safety reasons, studies about stress analysis of porous ductile materials are essential to understand their mechanical behaviour. Numerical modelling is performed in micro-structures using the concept of representative volume element (RVE) where the matrix is considered as an ideally plastic material governed by the von Mises model with isotropic hardening, while inclusions are adopted as very stiff elastic materials. Also, fracture and contact finite elements are used to model the phase debonding. Different distributions of voids and inclusions are assumed in the RVE domain to investigate their influences on the proposed analyses. We conclude, for instance, that the concentration of voids in the RVE decreases its loading capacity. On the other hand, we show in the numerical examples that the RVEs containing random distributions of voids present loading capacity improved when compared to the RVEs containing symmetric distributions of voids. Moreover, the results show that the insertion of reinforcements into porous ductile media has limited efficiency when dealing with high values of loading.