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

We have studied a model square-rectangular proper ferroelastic transition in an inhomogeneous stress field σ(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 ${\mathrm{\sigma }}_{\mathit{c}}$(=0.801 in dimensionless units) exists such that for ‖σ(R ${)}_{\max }$>${\mathrm{\sigma }}_{\mathit{c}}$ 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.