A comparison of shape memory alloy constitutive models is presented. Two models are reviewed and compared for their capabilities at predicting the behavior of shape memory alloys through stress and temperature induced phase changes. The first model considered is a phenomenological one-dimensional constitutive model, originally proposed by Graesser and Cozzarelli, which provides the capability to model both the martensitic twinning hysteresis and martensite-austenite pseudo-elastic behavior typical of shape memory alloys. This is achieved by casting the parameters used to define the behavior of the model in a temperature dependent form. The model is formulated using strain rate dependence to define the inelastic strain response of the shape memory alloy. Constitutive laws are formulated as strain rate dependent, using the concepts of endochronic plasticity resulting in an incremental form suitable for rate independent finite element analysis. The second model considered is typical of the family of thermomechanical constitutive laws based on the work of Tanaka and Liang. Shape memory alloy behavior is modeled considering the transformation kinetics based on the free energy, martensite fraction, and the laws of thermodynamics. An internal variable is used to represent the volume fraction of martensite in both twinned and aligned variants. The resulting constitutive law has been demonstrated to represent the varied thermomechanical behaviors of shape memory alloys when transforming between allowable phases.
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