• DOI:10.1007/s00332-023-09888-z
• Corpus ID: 246015380

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

@article{Alicandro2022CoarseGrainingOA,
  title={Coarse-Graining of a Discrete Model for Edge Dislocations in the Regular Triangular Lattice},
  author={Roberto Alicandro and Lucia De Luca and Giuliano Lazzaroni and Mariapia Palombaro and Marcello Ponsiglione},
  journal={Journal of Nonlinear Science},
  year={2022},
  volume={33}
}

• R. Alicandro, L. De Luca, +2 authors M. Ponsiglione
• Published 15 January 2022
• Materials Science
• Journal of Nonlinear Science

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 triangle detects the possible presence of an edge dislocation. We provide a Γ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Gamma $$\end{document}-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.