In recent years there has been considerable interest in understanding the response of wires and thin films composed of shape memory alloys in view of their relevance to important technological applications as stents, dental implants, actuators etc. Unfortunately, some of this research has been misdirected because of the failure to recognize the fact that the assumptions that are invoked to develop the approximations for wires, rods, beams and the like are wholly inadequate to describe the type of hysteretic behavior manifested by inelastic bodies in general and shape memory alloys, in particular. In this paper, we develop a theory that has reasonable physical underpinnings and also predicts response that is in keeping with the experimental results. The approach is based on the development of a special finite deformation beam theory using the notion of constrained response. Cyclic pure bending is considered and the results compared with available experimental data.
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