Hysteretic Systems with Internal Variables

Abstract

Hysteretic rate-independent constitutive laws are introduced within the framework of continuum thermodynamics with internal variables and revisited using concepts and arguments related to dynamical system theory. The evolution of internal variables is formulated either by a system of differential equations or by the associated phase flow. The restrictions implied by rate independence and thermodynamics are pointed out. Within this framework, the class of models with Masing hysteretic rules and Bouc endochronic relations are reviewed, and notions such as irreversibility, noninvertibility, and memory effects are discussed having recourse to different choices of internal variables. By introducing plastic strain as the internal variable, thermodynamic admissibility is proved for both models. However, while the processes with Masing rules exhibit a limited memory and are therefore noninvertible, the processes based on Bouc models are shown to have full memory and to be invertible though irreversible.