Recently, Fedelich and Zanzotto have developed a model for the nonisothermal pseudoelastic behaviour of a shape memory material and have conducted some numerical simulation experiments. We present a different method for the numerical solution and discuss it in comparison with their results.

We treat the mathematical properties of the one parameter version of the Mróz model for plastic flow. We present continuity results and an energy inequality for the hardening rule and discuss different versions of the flow rule regarding their relation to the second law of thermodynamics.

The rigid punch problem, a certain contact problem, leads to a noncoercive variational inequality. We show that its solution admits a directional derivative with respect to the data.

It is shown that the moving model, which is a variant of the Preisach model for hysteresis, possesses the wiping out property and is continuous in C[0,T] under natural assumptions.

A theorem due to Mayergoyz states that a hysteresis operator is a Preisach operator if and only if it has the congruency and wiping out property. We present a formal statement, proof and generalization of this result.

As shown by Krasnosel" skii, the classical Preisach model allows to construct a hysteresis operator Wbetween spaces of real functions of time. This construction, via the definition of a measure mü in the so-called Preisach plane, is recalled. Characterizations in terms of mü are given for several mapping and continuity properties of W in various function spaces, for the invertibility of W and for the corresponding mapping and continuity properties of the inverse.