Γ-convergence analysis of the nonlinear self-energy induced by edge dislocations in semi-discrete and discrete models in two dimensions-Reference-Cited by-同舟云学术

Γ-convergence analysis of the nonlinear self-energy induced by edge dislocations in semi-discrete and discrete models in two dimensions

Published:2024-02-20 Issue: Volume: Page:
ISSN:1864-8258
Container-title:Advances in Calculus of Variations
language:en
Short-container-title:

Author:

Alicandro Roberto¹^ORCID,De Luca Lucia²^ORCID,Palombaro Mariapia³^ORCID,Ponsiglione Marcello⁴^ORCID

Affiliation:

1. DIEI , Università di Cassino e del Lazio meridionale , via Di Biasio 43, 03043 Cassino (FR) , Italy

2. IAC-CNR , Istituto per le Applicazioni del Calcolo “M. Picone” , via dei Taurini 19, 00185 Roma , Italy

3. DISIM , Università dell’Aquila , Via Vetoio, 67100 L’Aquila , Italy

4. Dipartimento di Matematica , Università di Roma-I “La Sapienza” , Piazzale Aldo Moro 5, 00185 Roma , Italy

Abstract

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.

Publisher

Walter de Gruyter GmbH

Link

https://www.degruyter.com/document/doi/10.1515/acv-2023-0053/pdf

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