Modelling Nonlinear Dynamics of Shape-Memory-Alloys with Approximate Models of Coupled Thermoelasticity

Melnik, R.V.N. and Roberts, A.J.

ZAMM - Zeitschrift fur Angewandte Mathematik und Mechanik. 83, 93--104, 2003


We present a general methodology for constructing approximate models describing shape memory alloys dynamics. We base our discussion on a general three-dimensional model and the Falk-Konopka representation for the free energy function. By considering a one-dimensional counterpart of that model, we show that with little computational efforts we can reproduce successfully phase transition phenomena with our numerical scheme. The same scheme is applied in our code for the general case. Then, we describe a systematic approach to modelling SMA materials, and demonstrate that approach in deriving a centre-manifold-based low-dimensional model from the general three-dimensional model, preserving all main features of the dynamics. Computer algebra technique allows us to derive such models efficiently and with arbitrary degree of accuracy.