| Abstract: |
| We introduce nonlinear semi-discrete and discrete models for the elastic energy induced by a finite system of edge dislocations in two dimensions. We analyze the asymptotic behavior of the nonlinear elastic energy, as the lattice spacing (in the purely discrete model) and the core-radius (in the semi-discrete framework) vanish. We work within the dilute regime, corresponding to a finite number of effective singularities.
Joint work with Roberto Alicandro, Giuliano Lazzaroni, Mariapia Palombaro, Marcello Ponsiglione. |
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