On the bending of shape memory wires

In recent years there has been considerable interest in describing the response of shape-memory wires, thin films, beams, and other related structures in view of their technological relevance as parts of a plethora of devices such as actuators, stents, dental implants, and so on. Several analyses of the response of such materials have been carried out, but many of them have severe shortcomings because they neglect to pay adequate attention to the dissipative nature of such bodies. Other studies, in addition to the aforementioned deficiency, make kinematic assumptions that are flawed. We present a theoretical framework for the study of the finite deformation bending of shape-memory wires that takes cognizance of the dissipative nature of the body under consideration and also utilizes physically reasonable kinematic assumptions in the development of a finite deformation counterpart of the Bernoulli - Euler beam theory. The predictions of the theory are in keeping with the experimental results that are available.