A general theory of finite inelastic deformation of metals based on the concept of unified constitutive models

Abstract

First, a detailed survey of kinematics of finitely deformed inelastic solids is given. The concept is based on the multiplicative decomposition of the deformation gradient into elastic and inelastic parts. Since the intermediate configuration is chosen to be isoclinic as suggested by Mandel, this decomposition is unique. In a systematic manner, deformation tensors and strain tensors can be introduced. It is shown that a decomposition of the deformation rate tensor into elastic and inelastic parts is not unique and a kinematic relationship is established between two different definitions of the inelastic part of the deformation rate tensor. In this paper, all the kinematic quantities needed for the description of finite deformations with inelastic constitutive models are derived. Next, a general constitutive theory for finitely deformed viscoplastic materials is given for materials which are structurally isotropic. The elastic part of the model is assumed hyperelastic. The inelastic constitutive equations are based on the concept of internal variables. They are formulated on the intermediate configuration and mapped to the current configuration. The inelastic constitutive frame is specified for a model originally proposed by Brown, Kim and Anand. Further, the implications of small elastic strains are investigated. An improved approximation for the inelastic incompressibility constraint is derived. Numerical experiments for simple shear using different elastic models demonstrate the importance of a sufficiently accurate consideration of the inelastic incompressibility constraint.