A fractional approach to strain-gradient plasticity: beyond core-radius of discrete dislocations

2024/06/12 by Almi, Stefano, Caponi, Maicol, Friedrich, Manuel +1 · 5 citations
#26A33 #35R11 #49J45 #74C05 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2406.08023

Abstract

We derive a strain-gradient theory for plasticity as the Γ-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-α. As α goes to 0, we show that suitably rescaled energies Γ-converge to the macroscopic strain-gradient model of Garroni, Leoni, and Ponsiglione of 2010.

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