Hysteretic systems with internal variables

Hysteretic rate-independent constitutive laws are introduced within the fra mework of continuum thermodynamics with internal variables and revisited us ing concepts and arguments related to dynamical system theory. The evolutio n of internal variables is formulated either by a system of differential eq uations or by the associated phase flow. The restrictions implied by rate i ndependence 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 m emory effects are discussed having recourse to different choices of interna l variables. By introducing plastic strain as the internal variable, thermo dynamic admissibility is proved for both models. However, while the process es with Masing rules exhibit a limited memory and are therefore noninvertib le, the processes based on Bouc models are shown to have full memory and to be invertible though irreversible.