A GENERAL-THEORY OF FINITE INELASTIC DEFORMATION OF METALS BASED ON THE CONCEPT OF UNIFIED CONSTITUTIVE MODELS

First, a detailed survey of kinematics of finitely deformed inelastic solids is given. The concept is based on the multiplicative decomposit ion of the deformation gradient into elastic and inelastic parts. Sinc e the intermediate configuration is chosen to be isoclinic as suggeste d by Mandel, this decomposition is unique. In a systematic manner, def ormation tensors and strain tensors can be introduced. It is shown tha t a decomposition of the deformation rate tenser into elastic and inel astic parts is not unique and a kinematic relationship is established between two different definitions of the inelastic part of the deforma tion rate tenser. In this paper, all the kinematic quantities needed f or the description of finite deformations with inelastic constitutive models are derived. Next, a general constitutive theory for finitely d eformed viscoplastic materials is given for materials which are struct urally isotropic. The elastic part of the model is assumed hyperelasti c. The inelastic constitutive equations are based on the concept of in ternal variables. They are formulated on the intermediate configuratio n and mapped to the current configuration. The inelastic constitutive frame is specified for a model originally proposed by Brown, Kim and A nand. Further, the implications of small elastic strains are investiga ted. An improved approximation for the inelastic incompressibility con straint is derived. Numerical experiments for simple shear using diffe rent elastic models demonstrate the importance of a sufficiently accur ate consideration of the inelastic incompressibility constraint.