We consider a discrete model of planar elasticity where the particles, in the reference configuration, sit on a regular triangular lattice and interact through nearest-neighbor pairwise potentials, with bonds modeled as linearized elastic springs. Within this framework, we introduce plastic slip fields, whose discrete circulation around each tri-angle detects the possible presence of an edge dislocation. We provide a gamma-convergence analysis, as the lattice spacing tends to zero, of the elastic energy induced by edge dislocations in the energy regime corresponding to a finite number of geometrically necessary dislocations.

Coarse-Graining of a Discrete Model for Edge Dislocations in the Regular Triangular Lattice / R. Alicandro; L. De Luca; G. Lazzaroni; M. Palombaro; M. Ponsiglione. - In: JOURNAL OF NONLINEAR SCIENCE. - ISSN 0938-8974. - ELETTRONICO. - 33:(2023), pp. 33.0-33.0. [10.1007/s00332-023-09888-z]

Coarse-Graining of a Discrete Model for Edge Dislocations in the Regular Triangular Lattice

R. Alicandro;G. Lazzaroni;M. Palombaro;
2023

Abstract

We consider a discrete model of planar elasticity where the particles, in the reference configuration, sit on a regular triangular lattice and interact through nearest-neighbor pairwise potentials, with bonds modeled as linearized elastic springs. Within this framework, we introduce plastic slip fields, whose discrete circulation around each tri-angle detects the possible presence of an edge dislocation. We provide a gamma-convergence analysis, as the lattice spacing tends to zero, of the elastic energy induced by edge dislocations in the energy regime corresponding to a finite number of geometrically necessary dislocations.
2023
33
0
0
R. Alicandro; L. De Luca; G. Lazzaroni; M. Palombaro; M. Ponsiglione
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Utilizza questo identificatore per citare o creare un link a questa risorsa: https://hdl.handle.net/2158/1303165
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