Dynamics of Shape-Memory-Alloys: A Reduction Procedure for 3D Models

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

Proc. of the European Conference on Computational Mechanics: Solids, Structures and Coupled Problems in Engineering, W. Wunderlich, Ed.:  Munich, Germany,  pp. 1--18, 1999

Abstract:

Starting from a general Landau-type 3D model for the shape memory alloy dynamics we have developed a new mathematical "slow manifold" model that allows us to describe effectively the main features of the thermomechanical behaviour of CuAlNi alloys. A robust numerical procedure, developed in our earlier papers for the Falk model, has been generalised to this case. Results of the mathematical modelling of the thermomechanical fields in CuAlNi shape memory alloys are discussed with numerical examples.

Key words: shape memory alloys; centre manifold technique; Falk model; nonlinear thermomechanical coupling; phase transformations; reduction procedures for nonlinear mathematical models.