Phase Transitions in Shape Memory Alloys with Hyperbolic Heat Conduction and Differential-Algebraic Models

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

Computational Mechanics , 29, 16--26, 2002

Abstract:

The dynamics of phase transitions and hysteresis phenomena in materials with memory are described by a strongly nonlinear coupled system of partial differential equations which, in its generality, can be solved only numerically. Following principles of extended thermodynamics, in this paper we construct a new model for the description of this dynamics based on the Cattaneo-Vernotte law for heat conduction. Models based on the Fourier law follow from this general consideration as special cases. We develop a general procedure for the solution of the resulting systems by their reduction to differential-algebraic systems. Finally, a computational code for the numerical implementation of this procedure is explained in detail, and representative numerical examples are given.