Accepted Paper

Inserted: 12 jun 2024
Last Updated: 4 oct 2024

Journal: Mathematische Annalen
Year: 2024

Abstract:

We derive a strain-gradient theory for plasticity as the $\Gamma$-limit of discrete dislocation fractional energies, without the introduction of a core-radius. By using the finite horizon fractional gradient introduced by Bellido, Cueto, and Mora-Corral of 2023, we consider a nonlocal model of semi-discrete dislocations, in which the stored elastic energy is computed via the fractional gradient of order $1-\alpha$. As $\alpha$ goes to $0$, we show that suitably rescaled energies $\Gamma$-converge to the macroscopic strain-gradient model of Garroni, Leoni, and Ponsiglione of 2010.

Keywords: Gamma-convergence, edge dislocations, strain-gradient plasticity, Fractional model of discrete dislocations, Fractional and nonlocal gradients, Riesz potentials

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