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 / Alicandro, R.; De Luca, L.; Lazzaroni, G.; Palombaro, M.; Ponsiglione, M.. - In: JOURNAL OF NONLINEAR SCIENCE. - ISSN 0938-8974. - 33:2(2023). [10.1007/s00332-023-09888-z]
Coarse-Graining of a Discrete Model for Edge Dislocations in the Regular Triangular Lattice
De Luca L.;Ponsiglione M.
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.File | Dimensione | Formato | |
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