Discontinuous yielding transition of amorphous materials with low bulk modulus

The yielding transition of amorphous materials is studied with a two-dimensional Hamiltonian model that allows both shear and volume deformations. investigated as function the relative value bulk modulus $B$ respect to $\mu$. When ratio $B/\mu$ small enough, becomes discontinuous, yet reversible. If system driven at constant strain rate in coexistence region, spatially localized band observed while rest remains blocked. crucial role fluctuations origin this behavior clarified mean field version model.