Calculus of Variations and Geometric Measure Theory

R. Alicandro - L. De Luca - A. Garroni - M. Ponsiglione

Minimising movements for the motion of discrete screw dislocations along glide directions

created by deluca on 13 Mar 2017
modified by alicandr on 02 Mar 2018


Published Paper

Inserted: 13 mar 2017
Last Updated: 2 mar 2018

Journal: Calc. Var. Partial Differential Equations
Volume: 56:148
Year: 2017
Doi: 10.1007/s00526-017-1247-0


In ADGP a simple discrete scheme for the motion of screw dislocations toward low energy configurations has been proposed. There, a formal limit of such a scheme, as the lattice spacing and the time step tend to zero, has been described. The limiting dynamics agrees with the maximal dissipation criterion introduced in CG and predicts motion along the glide directions of the crystal. In this paper, we provide rigorous proofs of the results in ADGP, and in particular of the passage from the discrete to the continuous dynamics. The proofs are based on Gamma-convergence techniques.