Modelling of hysteresis in two-phase systems

Abstract

A mathematical formulation for the hysteretic behaviour of a two-phase thermo-elastic material undergoing stress-induced coherent martensitic phase transformations is proposed. The hysteresis effects are taken into account by making use of the second principle of thermomechanics and the postulate of realizability. The effective free energy density of the two-phase system is a result of homogenization of the piecewise quadratic potential adopted. The deformation process is formulated as an evolution variational inequality, which is finally solved as a sequence of linear complementarily problems. The answer to the question of existence and uniqueness of a solution to the problem is established. Results of numerical simulations for the shape-memory strips tested under uniaxiai tension are included. The strips are initially in an austenitic phase which under prescribed elongation transforms in a martensitic phase and subsequently, after releasing, returns to the initial state. The phase transformation occurs provided its driving force reaches some threshold value, and is accompanied by the energy dissipation and in homogeneous deformation. The results show the influence of the phase transformation, strain and boundary conditions on the propagation of the transformation front and the deformation mode of the specimen.