Shear bands as manifestation of a criticality in yielding amorphous solids

Abstract: Amorphous solids increase their stress as a function of an applied strain until a mechanical yield point whereupon the stress cannot increase anymore, afterwards exhibiting a steady state with a constant mean stress. In stress controlled experiments the system simply breaks when pushed beyond this mean stress. The ubiquity of this phenomenon over a huge variety of amorphous solids calls for a generic theory that is free of microscopic details. Here we offer such a theory: the mechanical yield is a thermodynamic phase transition, where yield occurs as a spinodal phenomenon. At the spinodal point there exists a divergent correlation length which is associated with the system-spanning instabilities (known also as shear bands) which are typical to the mechanical yield. The theory, the order parameter used and the correlation functions which exhibit the divergent correlation length are universal in nature and can be applied to any amorphous solids that undergo mechanical yield.