Coupled thermomechanical dynamics of phase transitions in shape memory alloys and related hysteresis phenomena

In this paper the nonlinear dynamics of shape memory alloy phase transformations is studied with thermo mechanical models based on coupled systems of partial differential equations by using computer algebra tools. The reduction procedures of the original model to a system of differential-algebraic-equations and its solution are based on the general methodology developed by the authors for the analysis of phase transformations in shape memory materials with low dimensional approximations derived from center manifold theory. Results of computational experiments revealing the martensitic-austenitic phase transition mechanism in a shape-memory-alloy rod are presented. Several groups of computational experiments are reported. They include results on stress- and temperature-induced phase transformations as well as the analysis of the hysteresis phenomenon. All computational experiments are presented for Cu-based structures.