Finite-strain solitons of a ferroelastic transformation in two dimensions

Interfaces in the 4mm-2mm ferroelastic transformation are treated to all orders in the nonlinearity of the Lagrangian strain tensor. The free-energy density has minimal form so that three of the six strains vanish identically, yielding a two-dimensional (square-rectangular) problem. The reduced form of the density contains no terms coupling the remaining strains; for free boundary conditions, a small volume decrease in the product state results from the geometrical nonlinearity of the strain tensor. An explicit procedure to obtain the displacement from the strains is given, and closed expressions for the displacements of the parent-product and product-product solitons are found. The extended form of the density includes a term coupling two strains, allowing a volume increase in the product state; the numerical solution of two second-order, ordinary differential equations followed by evaluation of two integrals gives the displacement. All three strains are nonzero in the wall region. For both densities, the displacements for solitons describing wall problems satisfy the two-dimensional wave equation (in the coordinates ${\mathit{x}}_1$ and ${\mathit{x}}_2$); the parent-product and product-product interfaces are parallel to the parent (110) and (11¯0) planes, and the product-product walls are twin boundaries.