Quantifying rate dependence of hysteretic systems

Hysteresis nonlinearities are formally defined as deterministic, rate-independent operators for a great variety of systems. Rate independence frequently occurs in problems in which the time scales of interest are much longer than the intrinsic time scales of the system. In this paper we propose a measure of rate dependence and numerically evaluate the corresponding metric for two rate-dependent systems, namely, a linearly viscous damper and a class of shape memory materials exhibiting thermomechanical behavior [1]. The rate-independent extended Bouc-Wen model of hysteresis [2] is used to validate the robustness of our rate-independence criterion. On the other hand, the shown rate dependence in shape memory materials working in nonisothermal conditions is associated with the ensuing thermomechanical coupling.