Influence of hardening and inhomogeneity on internal loops in pseudoelasticity

The paper is concerned with the mathematical modelling and computational simulation of hysteretic behaviour typically exhibited by shape memory alloys in the pseudoelastic temperature range, as observed by I. MULLER and his co-workers in experimental tests for CuZnAl monocrystals. The point of departure is the one-dimensional thermomechanical model due to I. MULLER and due to V. I. LEVITAS. The internal hysteresis loops are described by means of a discrete memory variable which can be handled by a monotone path rule. Existence end uniqueness of solutions is shown in the presence of hardening. We investigate the limit of vanishing hardening and vanishing material inhomogeneity and show that the limit depends on their relative size within the limit procedure. The analytical and numerical results show that under small hardening the phase transformation process is very sensitive to any inhomogeneities which may be present (e.g. geometric ones) or are developed in the two-phase system in the course of the loading/unloading sequences. Great differences in the local response at a material point and the system behaviour are observed, in particular the system displays internal loops only if the hardening is significantly larger than the material inhomogeneities. MSC (1991): 73C50, 80A99.