Cyclic Viscoplastic Constitutive Equations, Part I: A Thermodynamically Consistent Formulation

Abstract

Cyclic viscoplastic constitutive equations are increasingly used for the inelastic analysis of structures under severe thermomechanical conditions. The purpose of the paper is to show how the classical models can be modified in order to follow the general principles of thermodynamics with internal variables. Using the restrictive framework of standard generalized materials, the state variables associated to various kinds of kinematic and isotropic hardening are selected. The evolution equations for these internal variables are then formulated in a slightly less restrictive form. For each hardening process, the separation of the total plastic work into energy dissipated as heat and energy stored in the material is discussed in detail.