One-dimensional Quasi-static Nonisothermal Evolution of Shape-memory Material Inside the Hysteresis Loop

We study in this paper the quaistatic nonisothermal process of a one-dimensional bar consisting of a two-phase shape-memory material. The system of p.d.e.'s governing the evolution of the bar is obtained by means of a temperature-dependent hysteretic stress-strain law that we formulate as a "plasticity" criterion and a hysteresis operator. The constitutive theory is developed here on the basis of the mixture approach proposed by Muller [1] and of a natural extrapolation of the isothermal experimental data regarding the behavior of the material inside the hysteresis loop recently described Muller and Xu [2]. Numerical simulations are presented for three initial and boundary-value problems of interest with regard to uniaxial stretching experimental tests.