Martensitic textures: Multiscale consequences of elastic compatibility

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Abstract
We show that a free energy entirely in the order-parameter strain variable(s), rather than the displacement field, provides a unified understanding of martensitic textures. We use compatibility equations, linking the strain tensor components in the bulk and at interfaces, that induce anisotropic order-parameter strain interactions. These two long-range bulk/interface potentials, together with local compositional fluctuations, drive the formation of global elastic textures. Relaxational simulations show the spontaneous formation (and evolution under stress/temperature quenches) of equal width parallel twins, branched twins, and tweed, including characteristic scaling of twin width with twin length.