Cyclic effects in shape-memory alloys: A one-dimensional continuum model

We generalize the thermoelastic constitutive model of Abeyaratne and Knowles (1993, J. Mech. Phys. Solids 41, 541-571), and Abeyaratne et al. (1994, Int. J. Solids Structures 31, 2229-2249) so as to qualitatively model a variety of phenomena exhibited by shape-memory alloys in cyclic loading. The internal variable that is added to the model is meant to capture the idea that defects are precipitated during transformation and that these defects tend to make the nucleation of martensite easier.