Continuum theory of 4mm-2mm proper ferroelastic transformation under inhomogeneous stress

We have studied a model square-rectangular proper ferroelastic transition in an inhomogeneous stress field (R) with nonzero deviatoric stress component. This stress field can induce spatially heterogeneous transformations. Quasi-one-dimensional solutions for the lattice displacement fields u are derived both analytically and numerically for some special choices of stress functions. We find that the local instability is influenced by three factors: temperature, the magnitude of the applied stress, and the stress size. A critical strength c(=0.801 in dimensionless units) exists such that for (R)max>c a local transition can occur without an activation energy. The constraints of boundary conditions on the allowed solutions are also examined, and single-phase or twinned embryos may be formed through local transitions for free boundary conditions or fixed ends, respectively.