Non-linear structural modeling for life predictions: Physical mechanisms and continuum theories

Abstract

A review of several viscoplastic theories that incorporate isotropic hardening, directional hardening and additional effects due to non-proportional loading is presented. The equations reviewed are generalizations of the internal stress concept and use two internal state variables, namely the drag stress and the back stress variables. Theories that incorporate additional internal variables to model physical phenomena such as strain ageing have also been reviewed. Most of these constitutive equations employ isotropic evolutionary equations for the drag stress and nonlinear hardening rules for the back stress variable. The physical arguments to justify this procedure are given. The similarities between a wide number of formulations of flow and evolutionary equations, as well as the essential differences between them, are presented. Finally, it is shown how a careful examination of experimental behaviors, in conjunction with micromechanical considerations based on the physics of deformation, leads to the formulation of a more general unified framework.