Front migration for the dislocation strain in single crystals (Q1709633)

A single crystal is considered, i.e., a smooth 3-D elastic body containing a high density of point-defects and dislocations. In particular, the author considers prismatic dislocation loops which result as the primary manifestation of irradiated or highly-deformed crystals. He considers linearized elasticity and identifies the macroscopic dislocation-induced strain and its trace, directly related to the presence of dislocations, as the basic model variables. Further, he relies on a previously-introduced tensor version of a Cahn-Hilliard system in the context of incompatible linearized elasticity and considers the point-defects collapse into prismatic loops, yielding some well-formed microstructure. By means of a formal asymptotic analysis, he determines the front dynamics and obtains as a result a tensor version of Mullins-Sekerka dynamics. The associated gradient-flow formalism is also investigated.