We propose a new model describing the dynamics of wire made of shape memory alloys, by combining an elastic curve theory and the Ginzburg-Landau theory. The wire is assumed to be a closed curve and is not to be stretched with deformation. The derived system of nonlinear partial differential equations consists of a thermoelastic system and a geometric evolution equation under the inextensible condition. We also show that the system has dual variation structure as well as a straight material case. The structure implies stability of infinitesimally stable stationary state in the Lyapunov sense.
Part of the book: Shape Memory Alloys