Computational modeling of martensite: Emerging new paradigms

We present a brief review of spatial variations of the order parameter (e.g. strain, shuffle, etc.) in materials undergoing transitions such as ferroelastic martensites, shape memory alloys and magnetoelastics. We emphasize the usefulness of strain tensor and elastic compatibility constraint in providing key physical insights as well as a full description (including microstructure) of these materials. We outline applications of these ideas, in conjunction with recent experiments and computer simulations, in understanding strain textures such as twinning and transformation precursors.