Influence of hardening and inhomogeneity on internal loops in pseudoelasticity

The paper is concerned with the mathematical modelling and computational si mulation of hysteretic behaviour typically exhibited by shape memory alloys in the pseudoelastic temperature range, as observed by I. MULLER and his c o-workers in experimental tests for CuZnAl monocrystals. The point of depar ture 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. Ex istence end uniqueness of solutions is shown in the presence of hardening. We investigate the limit of vanishing hardening and vanishing material inho mogeneity and show that the limit depends on their relative size within the limit procedure. The analytical and numerical results show that under smal l hardening the phase transformation process is very sensitive to any inhom ogeneities which may be present (e.g. geometric ones) or are developed in t he two-phase system in the course of the loading/unloading sequences. Great differences in the local response at a material point and the system behav iour are observed, in particular the system displays internal loops only if the hardening is significantly larger than the material inhomogeneities. M SC (1991): 73C50, 80A99.