Anisotropic elasto-plastic constitutive equation for porous materials based on thermomechanical consideration

Abstract

Considering the effect of microscopic voids to macroscopic mechanical behavior is important because the fracture of ductile materials occurs through the initiation, the growth and the coalescence of voids. Anisotropy and softening are affected by the voids arrangement, and the growth bahavior of voids depends on not only stress and strain but their histories. The elasto-plastic constitutive equation which can represent anisotropy and compressivility of porous materials at once is presented in order to analyse deformation and damage evolution of the materials including voids to predict these phenomena. Damage tensor is employed to express decrease of effective cross-section area subjected to stress and its evolution equation is also derived to predict three dimensional growth of void. Thermomechanical consideration based on Clausius-Duhem's inequality is used to derive the model. Functional forms of dissipation inequality and dissipation potential are derived so that the anisotropic mechanical responce caused by the arrangement of voids is incorporated. The adequacy of presented model is evaluated through finite element analysis of unit cell assuming grid alignment of spherical voids. Initial and subsequent yield behavior are analysed with triaxial stress conditions. The presented model shows good agreement with finite element model for initial yield condition and relation between stress, strain and damage tensor.