A fractional approach to strain-gradient plasticity: beyond core-radius of discrete dislocations
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866915531287691264 |
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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 |
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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 |