Pattern formation in ferroelastic transitions

We study pattern formation in ferroelastic materials using the Ginzburg-Landau approach. Since ferroelastic transitions are driven by strain, the nonlinear elastic free energy is expressed as an expansion in the appropriate (i.e., order parameter) strain variables. However, the displacement Fields are the real independent variables. whereas the components of the strain tensor are related to each other through elastic compatibility relations. These constraints manifest as an anisotropic long-range interaction which drastically influences the underlying microstructure. The evolution of the microstructure is demonstrated for (i) a hexagonal-to-orthorhombic transition using a strain-based approach with explicit long-range interactions; and (ii) a cubic-to-tetragonal transition by solving the force-balance equations for the displacement fields.