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In this paper we show the emergence of polycrystalline structures as a resultof elastic energy minimisation. For this purpose, we introduce a variationalmodel for two-dimensional systems of edge dislocations, within the so-calledcore radius approach, and we derive the $\Gamma$-limit of the elastic energyfunctional as the lattice space tends to zero. In the energy regime underinvestigation, the symmetric and skew part of the strain become decoupled inthe limit, the dislocation measure being the curl of the skew part of thestrain. The limit energy is given by the sum of a plastic term, acting on thedislocation density, and an elastic term, which depends on the symmetricstrains. Minimisers under suitable boundary conditions are piece-wise constantantisymmetric strain fields, representing in our model a polycrystal whosegrains are mutually rotated by infinitesimal angles.

Derivation of Linearised Polycrystals from a 2D system of edge dislocations