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

Fuente: arXiv
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Hauptverfasser: Almi, Stefano, Caponi, Maicol, Friedrich, Manuel, Solombrino, Francesco
Format: Preprint
Veröffentlicht: 2024
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author Almi, Stefano
Caponi, Maicol
Friedrich, Manuel
Solombrino, Francesco
author_facet Almi, Stefano
Caponi, Maicol
Friedrich, Manuel
Solombrino, Francesco
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2406_08023
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle A fractional approach to strain-gradient plasticity: beyond core-radius of discrete dislocations
Almi, Stefano
Caponi, Maicol
Friedrich, Manuel
Solombrino, Francesco
Analysis of PDEs
26A33, 35R11, 49J45, 74C05
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.
title A fractional approach to strain-gradient plasticity: beyond core-radius of discrete dislocations
topic Analysis of PDEs
26A33, 35R11, 49J45, 74C05
url https://arxiv.org/abs/2406.08023