FINITE-ELEMENT ANALYSIS OF THE BEHAVIOR OF SHAPE-MEMORY ALLOYS AND THEIR APPLICATIONS

A nonlinear finite element procedure is developed which incorporates a thermodynamically derived constitutive law for shape memory alloy mat erial behavior. The constitutive equations include the necessary inter nal variables to account for the material transformations and are util ized in a one-dimensional finite element procedure that captures the u nique shape memory alloy responses of pseudoelasticity and of the shap e memory effect at an temperatures, stress levels and loading conditio ns. Detailed material properties for the alloy used are necessary for the analysis. The solution of the geometrically and physically nonline ar problem is achieved by application of a Newton's method in which a sequence of linear problems is numerically solved. Due to consistent l inearization, a quadratic rate of convergence is obtained. Several tes t cases are presented to illustrate the potential of the finite elemen t procedure. Cases simulating the stress-strain behavior of a bar of s hape memory alloy under simple uniaxial loading as well as restrained recovery responses at different temperatures compare well with experim ental and analytical results. Two further generalized applications are examined: the use of a shape memory alloy ring as a pipe connector an d eigenfrequency tuning of a composite beam with embedded shape memory wires. The results of these analyses correlate well with analytical r esults and the methodology for use of the finite element procedure in general cases is demonstrated. The finite element procedure is thus sh own to be a powerful tool for studying various applications of shape m emory alloys.