Constitutive equations for elastic-plastic materials at finite strain

Abstract

Constitutive equations are suggested for describing the behavior of elastic-plastic materials undergoing large strains. A special kinematical viewpoint is taken, so that the elastic and plastic deformation processes can be considered separately. This separation is also accommodated by a simplified thermodynamical theory of the deformation process. The elastic constitutive equation is written as a rate equation, after examining the interpretation of elastic isotropy in view of the particular kinematical description employed. To describe plastic deformation, a rate equation, which exhibits no dependence on the rate at which previous states have been traversed, is suggested. After the general relations have been put in appropriate form some simplifications based on physical assumptions are considered. The physical assumptions are based on the behavior of metals under large stress, high speed loading, such as in the penetration problem. Under these operating conditions, the thermoelastic effects dominate and plasticity plays a minor role. Consequently, a simple model of plastic deformation usually suffices. The analysis is presented in direct (matrix) notation and is valid for arbitrary stress states.