Mathematical and Numerical Analysis of Falk-Konopka-type Models for Shape Memory Alloys

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

Int. Journal of Differential Equations and Applications, 1A(3), 291--300, 2000

Abstract:

This paper is devoted to the development of mathematical theory of thermomechanical phase transitions. A hierarchy of mathematical models for smart materials and structures technologies is discussed in the context of models describing shape memory alloy dynamics. The authors analyze mathematical models resulting from the Falk-Konopka generalization of the Landau theory to the meso-scale level. Using center manifold techniques, the authors derive a low-dimensional model obtained directly from the three-dimensional Falk-Konopka model. The results of the theoretical analysis are supported by computational experiments.