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