Existence and stability of a screw dislocation under anti-plane deformation

We formulate a variational model for a geometrically necessary screw dislocation in an anti-plane lattice model at zero temperature. Invariance of the energy functional under lattice symmetries renders the problem non-coercive. Nevertheless, by establishing coercivity with respect to the elastic strain and a concentration compactness principle, we prove existence of a global energy minimiser and thus demonstrate that dislocations are globally stable equilibria within our model.

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