Statistical physics of the yielding transition in amorphous solids

The art of making structural, polymeric, and metallic glasses is rapidly developing with many applications. A limitation is that under increasing external strain all amorphous solids (like their crystalline counterparts) have a finite yield stress which cannot be exceeded without effecting a plastic response which typically leads to mechanical failure. Understanding this is crucial for assessing the risk of failure of glassy materials under mechanical loads. Here we show that the statistics of the energy barriers Delta E that need to be surmounted changes from a probability distribution function that goes smoothly to zero as Delta E=0 to a pdf which is finite at Delta E=0. This fundamental change implies a dramatic transition in the mechanical stability properties with respect to external strain. We derive exact results for the scaling exponents that characterize the magnitudes of average energy and stress drops in plastic events as a function of system size.