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

We derive a strain-gradient theory for plasticity as the \(\Gamma \) $\mathrm{\Gamma }$ -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 \(1-\alpha \) $1-\alpha$ . As \(\alpha \) $\alpha$ goes to 0, we show that suitably rescaled energies \(\Gamma \) $\mathrm{\Gamma }$ -converge to the macroscopic strain-gradient model of Garroni et la. (J Eur Math Soc (JEMS) 12:1231–1266, 2010).