Mechanism-Based Phenomenological Models for the Pseudoelastic Hysteresis Behavior of Shape Memory Alloys

A hierarchy of mechanism-based phenomenological models, comprising linear, piecewise-linear, and nonlinear springs and friction elements, are presented for the pseudoelastic damping behavior of Shape Memory Alloys. The constitutive equations and a method for identifying the model parameters from experimental hysteresis cycles are presented. A three-element model (comprising a spring and friction elements in parallel, all in series with a lead-spring) is the simplest model that captures the essence of the experimentally observed hysteresis behavior. Several more advanced models that better capture the experimental hysteresis behavior are presented. The use of piecewise-linear elements is found to significantly improve the ability of the model to simulate experimental data, but the improved predictive capability comes at the expense of increased complexity and some loss of generality, since the frictional parameters now depend on the amplitude of excitation. The predictive capability of the models can be improved, without introducing amplitude dependence, through the proper use of nonlinear springs and multiple spring/friction chains.