A microvoid evolution law involving change of void shape and micro/macroscopic analysis for damaged materials

In this paper, a microscopic damage model based on an ellipsoidal void for mixed-hardening materials is investigated under a particular coordinate. The change of void shape is considered in this model. The damage evolution law obtained from the model is affected by the void volume fraction, the void shape, and the triaxiality of the stress. The result is used to analyze the closing process of voids. Then, the damage evolution law is embedded into a new incremental elastoplastic constitutive equation for large deformation, and a damage constitutive equation is obtained. A numerical algorithm and finite element program for large elastoplastic deformation of damaged materials is developed, and is then applied to the analysis of the stress and damage distribution near the tip of the notch of the notched bar under uniaxial loading. Calculated results for the distribution of stress and damage show satisfactory agreement with experiment data.