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arXiv · 2305.02130

$\Gamma$-convergence analysis of the nonlinear self-energy induced by edge dislocations in semi-discrete and discrete models in two dimensions

Roberto Alicandro·Lucia De Luca·Mariapia Palombaro·Marcello Ponsiglione
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Abstract

We propose nonlinear semi-discrete and discrete models for the elastic energy induced by a finite systems 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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Roberto Alicandro, Lucia De Luca, Mariapia Palombaro, Marcello Ponsiglione. 2023-05-03. $\Gamma$-convergence analysis of the nonlinear self-energy induced by edge dislocations in semi-discrete and discrete models in two dimensions. https://arxiv.org/abs/2305.02130

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