An elastoplastic constitutive description based on an ellipsoidal void model

The constitutive behavior of metallic materials with numerous microvoids is investigated. The representative volume element of the materials is idealized as an incompressible ellipsoidal cell with a single ellipsoidal void at its center. Through the analysis of the microscopic velocity and strain fields of the void-cell model and making use of a nonclassical elastoplastic constitutive relation, the microscopic stresses of the ellipsoidal void-cell model are obtained, and it is further transformed to macroscopic stresses with the principle of energy coincidence. Combining the evolution of void growth with that of void nucleation, the void evolution rule is obtained. The obtained expression of macroscopic stress and the void evolution rule are embedded in a nonclassical elastoplastic constitutive description obtained from a simple mechanical model incorporating damage. The corresponding numerical algorithm and the finite element approach are developed and applied to the analysis of the elastoplastic response and the porosity of PD3 steel. The computed results show satisfactory agreement with experiments.