Shape Memory Materials: Mathematical Modelling and Numerical Simulations

Abstract

The shape memory effect is a physical property characteristic of numerous solids, including various metallic alloys and non-metailic solid materials like polymers. This property consists in an ability of a solid subject to plastic deformation to recover its original shape after an appropriate thermal treatment (possibly complemented by a mechanical loading). The effect has already been discovered in the mid-thirties, but an explosive development of the interest in it, as well as understanding of its enormous applicability range date from the late sixties and are related to the discovery of extraordinarily strong and, equally, preserved in time, shape memory property of Ti-Ni alloy (Nitinol), cf. [6,29]. The same type of effects has been discovered also in many other metallic alloys. There exists, in- between, an extensive literature devoted to the physics of shape memory effect (cf. [6,17,28]) and its applications (cf. [3,6,12]). It is not our objective to give any overview of these aspects. What we are going to expose is related to the most common characteristic features of the dynamical processes in materials exhibiting shape memory and then to construct phenomenological models capable of forecasting the developments in space and time both qualitatively and quantitatively. Since the behavior is strongly affected by the choice of a specific class of materials, we shall focus on metallic alloys, with Nitinol in mind, in particular. We shall discuss the applicability range of the models proposed and shall show some typical results of numerical experiments which visualize their forecasting value.