<title>Constitutive model for shape memory alloys and its use in design and finite element analysis</title>

Abstract

A constitutive model for predicting the thermomechanical behavior of Shape Memory Alloys (SMAs) has been developed and validated. The model uses an approach similar to Brinson, 1 Liang and Rogers, 2 and Tanaka. 3 It links key thermomechanical variables: stress, strain, temperature, and martensite fraction. A basic differential form for the SMA constitutive behavior, developed by Tanaka, forms the foundation of the model. The model is completed with a definition of the rules governing the behavior of martensite fraction. Like Brinson, the model distinguishes between de-twinned and twinned martensite. The phase transition temperatures are assumed to be a linear function of applied stress. The forward and reverse phase transformations are described by piecewise exponential functions. There are a number of parameters in the model that need to be determined using experimental data. The critical transformation temperatures are determined by resistivity measurements. All other parameters are determined by mechanical tension testing followed by nonlinear least-squares estimations. Mechanical testing consisted of displacement controlled, tension tests on Nitinol wires at several temperatures. The effectiveness of this model is demonstrated by its use in the design of an SMA actuated robotic arm. The constitutive model is used in conjunction with a lumped heat transfer model, a kinematic model, and a dynamic model to predict the behavior of the arm. Comparison between predictions and experimentally observed behavior is very good indicating a sound constitutive model. The model is also built into a finite element code that simulates pseudoelastic SMA behavior. The code considers geometric and material nonlinearities. The behavior of a simple pseudoelastic device is shown to be well predicted by the finite element code.