Here we will present a simplification of the form of one popular shape memory alloy (SMA) constitutive model. This simplification allows a more compact written form and hence easier calculations with the one-dimensional SMA constitutive law first developed by Tanaka, later modified by Liang and Rogers, and again by Brinson. In addition, a new derivation of the model will be given based on micromechanics. In this context, comparisons between the Tanaka and two other models will be presented and implications discussed. It will be shown that the constitutive models are in fact quite similar, and that the important distinction between these SMA models is primarily in the formulation of the transformation kinetics. Several examples will be presented utilizing the models.

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In this paper the active control of beam deflection through heating and cooling of Shape Memory Alloy (SMA) wires is examined. A phenomenological constitutive law for SMA wires is coupled with beam theory to provide predictions of beam shape upon temperature change in the SMA actuator. Both the linear and nonlinear beam theory are presented, enabling calculation of large deflections. Examples for a single wire attached at the tip of a uniform beam are given, but the procedure can easily be generalized for other configurations and utilized in control algorithms. Issues of design constraints for shape control with shape memory wires are addressed and the model is qualitatively verified by experiments.