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In dislocation-free martensites the components of the elastic strain tensorare constrained by the Saint-Venant compatibility condition which guaranteescontinuity of the body during external loading. However, in dislocatedmaterials the plastic part of the distortion tensor introduces a displacementmismatch that is removed by elastic relaxation. The elastic strains are then nolonger compatible in the sense of the Saint-Venant law and the ensuingincompatibility tensor is shown to be proportional to the gradients of the Nyedislocation density tensor. We demonstrate that the presence of thisincompatibility gives rise to an additional long-range contribution in theinhomogeneous part of the Landau energy functional and to the correspondingstress fields. Competition amongst the local and long-range interactionsresults in frustration in the evolving order parameter (elastic) texture. Weshow how the Peach-Koehler forces and stress fields for any distribution ofdislocations in arbitrarily anisotropic media can be calculated and employed ina Fokker-Planck dynamics for the dislocation density. This approach representsa self-consistent scheme that yields the evolutions of both the order parameterfield and the continuous dislocation density. We illustrate our method bystudying the effects of dislocations on microstructure, particularly twinneddomain walls, in an Fe-Pd alloy undergoing a martensitic transformation.

Defect-induced incompatibility of elastic strains: dislocations within the Landau theory of martensitic phase transformations