We propose nonlinear semi-discrete and discrete models for the elastic energy induced by a finite system of edge dislocations in two dimensions. Within the dilute regime, we analyze the asymptotic behavior of the nonlinear elastic energy, as the core-radius (in the semi-discrete model) and the lattice spacing (in the purely discrete one) vanish. Our analysis passes through a linearization procedure within the rigorous framework of Γ-convergence.
Γ-convergence analysis of the nonlinear self-energy induced by edge dislocations in semi-discrete and discrete models in two dimensions / Alicandro, R.; De Luca, L.; Palombaro, M.; Ponsiglione, M.. - In: ADVANCES IN CALCULUS OF VARIATIONS. - ISSN 1864-8258. - 18:1(2025), pp. 1-23. [10.1515/acv-2023-0053]
Γ-convergence analysis of the nonlinear self-energy induced by edge dislocations in semi-discrete and discrete models in two dimensions
Alicandro R.;
2025
Abstract
We propose nonlinear semi-discrete and discrete models for the elastic energy induced by a finite system of edge dislocations in two dimensions. Within the dilute regime, we analyze the asymptotic behavior of the nonlinear elastic energy, as the core-radius (in the semi-discrete model) and the lattice spacing (in the purely discrete one) vanish. Our analysis passes through a linearization procedure within the rigorous framework of Γ-convergence.| File | Dimensione | Formato | |
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