Dislocations in nonlinear nonlocal media: Martensitic embryo formation

A model is developed for determining the stress and strain fields of an array of slip dislocation defects in a two-dimensional elastic medium with a highly nonlinear and nonlocal energy functional. The medium serves as a model for an elastic system in the vicinity of a martensitic structural phase transformation, in the high-temperature regime where the metastable product phase first acquires local stability. The dislocation array is a model of a candidate site for heterogeneous nucleation of martensite. The slip dislocation defects are included in the continuum by means of a static, external `topological' field superimposed on the conventional elastic displacement field. The results indicate that a fully transformed martensitic region of mesoscopic size is stabilized by the nonlinear elastic field of the dislocations at temperatures substantially higher than the equilibrium temperature T<sub>0</sub>, consistent with the Kaufman-Cohen `preexisting embryo' hypothesis.