Preprint

Inserted: 3 may 2023
Last Updated: 3 may 2023

Year: 2023

Abstract:

We propose nonlinear semi-discrete and discrete models for the elastic energy induced by a  finite system of edge dislocations in two dimensions. Within the dilute regime, we analyze the asymptotic behavior of the nonlinear elastic energy, as the core-radius (in the semi-discrete model) and the lattice spacing (in the purely discrete one) vanish. Our analysis passes through a linearization procedure within the rigorous framework of $\Gamma$-convergence.

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