In this work we study the depinning and the dynamics of disordered elastic systems which de nes a broad class of systems from interfaces (like magnetic or ferroelectric domains walls) to periodic structures (like vortex lattices in type II superconductor, colloids or Wigner crystals). In these systems, the competition between the elasticity of the structure that wants to impose a perfect order and disorder produces a rich phase diagram. We use large-scale numerical simulations, in which we speci cally focus on 2D superconductor vortex lattices. Two types of depinning are observed when the lattices are driven by a uniform force : plastic and elastic depinning. We mainly focus on the elastic depinning obtained when the pinning is weak. Using a scaling law analysis at both zero and nonzero temperature we show that the depinning transition is continuous near the depinning threshold. Various critical exponent are evaluated such as the and exponents characterizing the force and temperature dependances of the velocity or the exponent characterizing the divergence of the correlation length of the system. A simple viscoelastic model allowing to describe plasticity in periodic structures driven over a strong disordered medium is also developed. A wide variety of dynamical behaviors, similar to those observed on a larger scale in periodic systems, can be extracted from such a model. An elastic or plastic depinning is observed, hysteresis is measured in the case of elastic depinning, while chaos is detected for plastic depinning.
