Form for the Relation Between Stress and Finite Elastic and Plastic Strains under Impulsive Loading

Abstract

This paper derives a form for the relation between stress and finite elastic and plastic strains. The finite elastic and plastic contributions to large deformation are defined assuming that these arise from distinct elastic and plastic mechanisms of deformation. This assumption is mathematically represented by distinct relations between the elastic and plastic deformations and the state of stress. The choices for these relations are based on the theory of perfect elasticity and on the theory of quasistatic plasticity, but with modifications that permit the application to large strains and to dynamic situations. The expression for the dependence of the plastic deformation on the stress is explicitly strain‐rate dependent. For simplicity the material is assumed to be isotropic. Constitutive relations are developed for the problem of one‐dimensional stress‐wave propagation.