Martensitic variant

A martensitic variant is one of the lattice deformations corresponding to the low-temperature crystal phase. The parent crystal's discrete symmetries generate different variants. In a nonlinear elasticity model each representative $U_i$ supplies a hyperelastic energy well $SO(3)U_i$. A representative need not itself be a symmetric stretch tensor; multiplication by a proper rotation leaves the same well.

Deformation twinning joins differently oriented crystal variants across a coherent interface. In a piecewise affine nonlinear elasticity model the two deformation gradients must differ by $a\otimes N$, where $N$ is the reference interface normal. The Hadamard jump condition gives this requirement from continuity along every interface tangent. Compatible alternating layers can then make a mixture of variants whose macroscopic shape differs from either variant alone.