Computing dynamics of copper-based SMA via center manifold reduction of 3D models

In this work, we present a reduction procedure for 3D models describing phase transformations in copper-based shape memory alloys (SMAs) and develop a robust numerical algorithm for the computational analysis of thin single-crystal slabs of these alloys. Starting from a general Landau-type 3D model for the SMA dynamics we have developed a new mathematical 'slow manifold' model that allows us to describe effectively the main features of the thermomechanical behaviour of CuAlNi alloys. Results of the mathematical modelling of the thermomechanical fields in CuAlNi SMAs are discussed with numerical examples