Depinning transition in material failure, Barkhausen effect and contact line motion

The motion of an elastic manifold in a random medium is involved in many physical situations. If the driving force is increased, the interplay between elasticity and disorder results in a transition from a stable manifold pinned by the defects to a propagating one, also referred to as a depinning transition.

Here, we show how the theoretical concepts associated with such a transition can be applied to describe the behavior of three different systems: the propagation of cracks in heterogeneous materials, the motion of ferromagnetic domain walls leading to the Barkhausen effect and the motion of contact lines of liquids on solid substrates.