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We consider a singularly-perturbed two-well problem in the context of planargeometrically linear elasticity to model a rectangular martensitic nucleus inan austenitic matrix. We derive the scaling regimes for the minimal energy interms of the problem parameters, which represent the {shape} of the nucleus,the quotient of the elastic moduli of the two phases, the surface energyconstant, and the volume fraction of the two martensitic variants. We identifyseveral different scaling regimes, which are distinguished either by theexponents in the parameters, or by logarithmic corrections, for which we havematching upper and lower bounds.

Energy scaling laws for geometrically linear elasticity models for microstructures in shape memory alloys