Shape-memory alloys are special materials that undergo a martensitic phase transition, that is, a diffusionless first order solid-solid phase transformation. Pattern formation in shape-memory alloys is often studied in the framework of the calculus of variations. The formation of microstructures is typically explained as result of a competition between a bulk elastic energy and a higher order surface energy. I shall discuss some recent analytical results on such variational problems, in particular regarding needle-like microstructures and stress-free inclusions.
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