Serial deformation maps and elasto-plastic continua

Abstract

This paper deals with the kinematics of finite plastic deformation. The starting point is E.H. Lee’s multiplicative decomposition of the deformation gradient into its elastic and plastic parts. We diverge from Lee’s (and others’) derivation of the deformation rate and spin tensors and prove that the elastic and plastic deformation rate and spin tensors are additive. It is then shown that the elastic and plastic strains are also additive and equal to the total strain. A central result, and a major deviation from continuum mechanics, is that not one, but two deformation maps are necessary for the constitutive response in elasto-plasticity. The two-map decomposition is then extended to the n-th order, and additivity is shown there as well. Elastoplastic constitutive equations in large deformation are presented and discussed in the context of path-dependent (endochronic) plasticity.