Internal State Variable Theory

Abstract

Many practical problems of interest deal with irreversible, path dependent aspects of material behavior, such as hysteresis due to plastic deformation or phase transition, fatigue and fracture, or diffusive rearrangement. Some of these processes occur so slowly and so near equilibrium that attendant models forego description of nonequilibrium aspects of dissipation (e.g., grain growth). On the other hand, some irreversible behaviors such as thermally activated dislocation glide can occur farther from equilibrium with a spectrum of relaxation times. The fact that quasi-stable, nonequilibrium configurations of defects can exist in lattices at multiple length scales, combined with the long range nature of interaction forces, presents an enormous challenge to the utility of high fidelity, high degree of freedom (DoF) dynamical models that employ atomistic or molecular modeling methods. For example, analyses of simple crystal structures using molecular dynamics have now reached scales on the order of microns, but are limited to rather idealized systems such as pure metals and to small time durations of the order of nanoseconds. High fidelity analyses of generation, motion and interaction of line defects in lattices based on discrete dislocation dynamics, making use of interactions based on linear elastic solutions, cover somewhat higher length scales and longer time scales, but are also limited in considering realistic multiphase, hierarchical microstructures. Crystal plasticity as well cannot be used for large scale finite element simulations, for example, crash simulations of a vehicle into a barrier.