Discrete models of dislocations and their motion in cubic crystals

A discrete model describing defects in crystal lattices and having the standard linear anisotropic elasticity as its continuum limit is proposed. The main ingredients entering the model are 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 are given for crystals with cubic symmetry: sc (simple cubic), fcc, and bcc. 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 are also numerically observed. Cracks can be created and propagated by applying a sufficient load to a dipole formed by two edge dislocations.