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

  • Roberto Alicandro ORCID logo , Lucia De Luca ORCID logo EMAIL logo , Mariapia Palombaro ORCID logo and Marcello Ponsiglione ORCID logo
Published/Copyright: February 20, 2024

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.


Communicated by Ulisse Stefanelli


Funding statement: Roberto Alicandro, Lucia De Luca, and Mariapia Palombaro are members of the Gruppo Nazionale per l’Analisi Matematica, la Probabilità e le loro Applicazioni (GNAMPA) of the Istituto Nazionale di Alta Matematica (INdAM).

Acknowledgements

The authors thank G. Lazzaroni for interesting and fruitful discussions on discrete nonlinear elasticity models.

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Received: 2023-05-03
Accepted: 2023-10-02
Published Online: 2024-02-20
Published in Print: 2025-01-01

© 2024 Walter de Gruyter GmbH, Berlin/Boston

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