  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, 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.
