A THERMODYNAMICALLY CONSISTENT FRAMEWORK FOR THEORIES OF ELASTOPLASTICITY COUPLED WITH DAMAGE

A unified framework for coupled elastoplastic and damage theories is developed. A rigorous thermodynamic procedure is followed that is sufficiently general to include anisotropic plasticity and anisotropic damage formulations. The concept of effective stress is the critical mechanism for coupling these theories, Yield and damage functions, constructed of homogeneous functions of degree one, are shown to satisfy thermodynamic restrictions. The principle of maximum entropy provides the evolutionary relations, the loading and unloading conditions, and the convexity of the undamaging elastic domain. The plastic and damage variables evolve normal to their respective surfaces which for plasticity corresponds to an associative flow for plastic strain. This general framework is shown to be sufficiently general lo encompass several popular theories for plasticity and damage. Limitations of some existing damage theories are discussed. The performance of two specific coupled formulations are illustrated by replicating the experimental behavior of an aluminum alloy.