A discrete model describing defects in crystal lattices and having the standard linear anisotropic elasticity as its continuum limit was proposed. The main ingredients entering the model were the elastic stiffness constants of the material and a dimensionless periodic function that restores the translation invariance of the crystal and influences the Peierls stress. Explicit expressions were given for crystals with cubic symmetry: simple cubic, face-centered cubic and body-centered cubic. Numerical simulations of this model with conservative or damped dynamics illustrate static and moving-edge and screw dislocations, and describe their cores and profiles. Dislocation loops and dipoles were also numerically observed. Cracks could be created and propagated by applying a sufficient load to a dipole formed by two edge dislocations.

Discrete Models of Dislocations and their Motion in Cubic Crystals. A.Carpio, L.L.Bonilla: Physical Review B, 2005, 71[13], 134105 (10pp)