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A nonlinear finite element procedure is developed which incorporates a thermodynamically derived constitutive law for shape memory alloy material behavior. The constitutive equations include the necessary internal variables to account for the material transformations and are utilized in a one-dimensional finite element procedure that captures the unique shape memory alloy responses of pseudoelasticity and of the shape memory effect at all temperatures, stress levels and loading conditions. Detailed material properties for the alloy used are necessary for the analysis. The solution of the geometrically and physically nonlinear problem is achieved by application of a Newton's method in which a sequence of linear problems is numerically solved. Due to consistent linearization, a quadratic rate of convergence is obtained.

Several test cases are presented to illustrate the potential of the finite element procedure …