A mathematical model is constructed for the modelling of two di- mensional thermo-mechanical behavior of shape memory alloy patches. The model is constructed on the basis of a modified Landau-Ginzburg theory and includes the coupling effect between thermal and mechanical fields. The free energy functional for the model is exemplified for the square to rectangular transformations. The model, based on nonlinear coupled partial differential equations, is reduced to a system of differential-algebraic equations and the backward differentiation methodology is used for its numerical analysis. Computational experiments with representative distributed mechanical loadings are carried out for patches of different sizes to analyze thermo-mechanical waves, coupling effects, and 2D phase transformations.
Wang, Linxiang and Melnik, Roderick V.N., "Dynamics of Shape Memory Alloys Patches with Mechanically Induced Transformations" (2006). Mathematics Faculty Publications. 35.
This article was originally published in Discrete and Continuous Dynamical Systems, 15(4): 1237-1252.