A multi-variant martensitic phase transformation model: formulation and numerical implementation Original Research Article

The development of models for shape memory alloys and other materials that undergo martensitic phase transformations has been moving towards a common generalized thermodynamic framework. Several promising models utilizing single martensitic variants and some with multiple variants have appeared recently. In this work we develop a model in a general multi-variant framework for single crystals that is based upon lattice correspondence variants and the use of dissipation arguments for the generation of specialized evolution equations. The evolution equations that appear are of a unique nature in that not only are the thermodynamic forces restricted in range but so are their kinematic conjugates. This unusual situation complicates the discrete time integration of the evolution equations. We show that the trial elastic state method that is popular in metal plasticity is inadequate in the present situation and needs to be replaced by a non-linear programming problem with a simple geometric interpretation. The developed integration methodology is robust and leads to symmetric tangent moduli. Example computations show the behavior of the model in the pseudoelastic range. Of particular interest is the fact that the model can predict the generation of habit plane-like variants solely from the lattice correspondence variants; this is demonstrated through a comparison to the experimental work of Shield [J. Mech. Phys. Solids 43 (1995) 869].