Determinação da resistência mecânica de materiais porosos plasticamente ortotrópicos via homogeneização computacional

Abstract

This work evaluates the strength of porous elastoplastic materials with orthotropic matrix, which is assumed to be insensitive to both the mean stress and the strain rate, via computational homogenization procedure. The simulations are carried out on cubic elementary cells, employing the finite element method under small strains. Each elementary cell represents an agregate composed of a non-hardening elastoplastic matrix with symmetrically distributed voids (spherical or cylindrical), considering distinct porosity and matrix anisotopy levels. From the numerical analysis, effective yield surfaces are build imposing displacement-based boundary conditions while keeping the macroscopic stress triaxiality constant throughout the deformation process. After reaching an asymptotic macroscopic stress state, the macroscopic stress components are calculated from standard volume average from their microscopic counterpart. The numerical results are compared with analytical solutions (upper, quasi-lower and lower limits) available in the literature and one developed in the context of this work to materials with Hill matrix and cylindrical voids. Furthermore, aiming at reducing the difference between the numerical and theoretical results, which is due to difference regarding the geometry of both numerical and theoretical eleementary cells, heuristic modifications are proposed to the analytical models. Therefore, it is expected that this work contributes to the understanding regarding the mechanical behavior of porous material with plasticaly anisotropic matrix, which for instance, is the case of materials and structures produced by additive manufacturing.