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One-dimensional sharp-phase-front-based continuum models of phase transformations in shape memory alloys

The issue of phase transformations in shape memory alloys is revisited in the 1D context. We focus on problems where there is a sharp interface between the two phase of austenite and martensite. Apart from the usual conservations equations, it is proposed that an extra equation be used to render the system of equations complete, when a first-order transition is considered. Seen within this context, the following two approaches can be derived as special cases: (i) Leo et al approach where the phase boundary temperature is taken to be linearly related to the stress, (ii) Abeyaratne and Knowles approach where a kinetic relation is assumed. Certain other implications of the new approach are discussed in light of these special cases.