Figure 5. Depinning theory in the amorphous plasticity context.

(a) Depinning theory describes the motion of an elastic interface (here a one-dimensional front) in a random potential. The circles represent the (plastic) displacement of each point in the front. The front is subject to an applied force that causes it to move but elements of the front are pinned locally and need to overcome energy barriers. The different elements of the front are connected by springs so that if one pinned site overcomes the energy barrier it is pulling its nearest neighbours (and only them). (b) If the interactions are long range, different pinned elements of the front interact with distant elements and the actual structure of the front becomes immaterial. (c) In this case, there is no real difference between the equations that describe a front and the equations that describe the interaction of some collection of pinning sites distributed in the material. A simple model of plasticity31, which belongs to the depinning universality class, has been shown to describe the dynamics of an amorphous solid under shear where ‘shear transformation zones' or ‘weak spots' are dispersed in the material and affect each other with long-range elastic interactions.