Free Boundary Conditions at Austenite-Martensite Interfaces.

A mathematical model is presented for the dynamical strain-stress response of shape memory wires. This model is based on a free boundary problem for the heat equation which incorporates bistable potentials together with a physical constant, independent of stress or temperature, which accounts for mechanically dissipative processes. An expression in closed form is derived for one of the most important observables, namely the width of the hysteresis loops as a function of the elongation rates. Excellent agreement with experimental results is observed.