  We study a generalization of the fully overdamped Frenkel-Kontorova model in
dimension $n\geq 1.$ This model describes the evolution of the position of each
atom in a crystal, and is mathematically given by an infinite system of coupled
first order ODEs. We prove that for a suitable rescaling of this model, the
solution converges to the solution of a Peierls-Nabarro model, which is a
coupled system of two PDEs (typically an elliptic PDE in a domain with an
evolution PDE on the boundary of the domain). This passage from the discrete
model to a continuous model is done in the framework of viscosity solutions.
