Calculus of Variations and Geometric Measure Theory

R. Alicandro - L. De Luca - M. Palombaro - M. Ponsiglione

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

created by deluca on 03 May 2023



Inserted: 3 may 2023
Last Updated: 3 may 2023

Year: 2023


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 $\Gamma$-convergence.