Microstructures in Low-Hysteresis Shape Memory Alloys: Scaling Regimes and Optimal Needle Shapes

For certain martensitic phase transformations, one observes a close relation between the width of the thermal hysteresis and the compatibility of two phases. This observation forms the basis of a theory of hysteresis that assigns an important role to the microstructures in the transition layer and their energetics (Zhang et al., Acta Mater 57(15), 4332–4352, 2009). We study microstructures for almost compatible phases in the context of nonlinear elasticity. Using a scalar valued ansatz we show that one expects a transition from uniform to branched patterns for various typical models of the surface energy. We subsequently consider needle-type transition layers and study quantitative differences between hard and soft austenite, and between twins of different martensitic variants.