A Rate-Independent Constitutive Theory for Finite Inelastic Deformation

Abstract

A rate-independent constitutive theory for finite inelastic deformation is formulated in terms of the symmetric Piola-Kirchhoff stress, the Lagrangian strain, and a kinematic tensor which describes inelastic or microstructural effects. Assumptions of (a) continuity in the transition from loading to neutral loading, (b) consistency, and (c) nonnegative work in closed cycles of deformation, lead to simplification of the theory. The response is described by two scalar functions — a stress potential and a loading function. The theory can describe isotropic or anisotropic response, and allows for hardening, softening, or ideal behavior. It may also be appropriate to describe the response of porous materials, such as metals, rocks and ceramics, and also the evolution of damage.