Three-dimensional mathematical models of phase transformation kinetics in shape memory alloys

Mahapatra, D.R. and Melnik, R.V.N.

Dynamics of Continuous, Discrete and Impulsive Systems, Series B: Applications and Algorithms,  Supplementary Volume, DCDIS4: ISSN 1492-8760, 557--562, 2005


We develop a 3D mathematical model based on a fully coupled free energy representation of multi-variant martensitic phase transformations and discuss its computational implementation. In particular, we derive a finite element model by using variational minimization involving (1) momentum conservation (2) heat conduction with convective terms but dominated by stress-driven dissipation, and (3) first-order phase kinetics. We provide numerical results on the simulation of transient stress-driven phase field evolution in a NiAl thin film.