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

Almi S, Caponi M, Friedrich M, Solombrino F (2024)

Publication Type: Journal article

Publication year: 2024

Journal

Mathematische Annalen Springer Verlag (Germany)

DOI: 10.1007/s00208-024-03020-6

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 et al. (Adv Calc Var 17:1039–1055, 2024), 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 et la. (J Eur Math Soc (JEMS) 12:1231–1266, 2010).

Authors with CRIS profile

Manuel Friedrich Professur für Angewandte Mathematik (Angewandte Analysis)

Involved external institutions

Università degli Studi di Napoli Federico II IT Italy (IT)

How to cite

APA:

Almi, S., Caponi, M., Friedrich, M., & Solombrino, F. (2024). A fractional approach to strain-gradient plasticity: beyond core-radius of discrete dislocations. Mathematische Annalen. https://doi.org/10.1007/s00208-024-03020-6

MLA:

Almi, Stefano, et al. "A fractional approach to strain-gradient plasticity: beyond core-radius of discrete dislocations." Mathematische Annalen (2024).

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