Modelling Dynamics of Shape-Memory-Alloys via Computer Algebra

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

Mathematics and Control in Smart Structures, Proc. of SPIE, Vol. 3667,  Ed.: V.V. Varadan, 290-301, 1999

Abstract:

In this paper we present results on numerical studies of the martensitic-austenitic phase transition mechanism in a large shape-memory-alloy rod. For the first time, we present a new efficient numerical model based on a low-dimensional reduction of the general three-dimensional model for shape memory alloys. The resulting system is reduced to a system of differential-algebraic equations and is solved by using second-order accurate spatial difference discretizations on staggered grids. Three groups of experiments are reported. They include results on stress- and temperature- induced phase transformations as well as the analysis of the hysteresis phenomenon. All computational experiments are presented for Cu-based structures.

Key words: hysteresis modeling; nonlinear thermomechanical coupling; mathematical models of phase transformations; differential-algebraic systems; shape memory alloys; numerical analysis; stress and temperature induced phase transformations; low dimensional modeling and centre maniforld theory; Landau-Devonshire-Ginzburg free energy function; computer algebra; invariant manifolds.

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