Volume-shear coupling in a mesoscopic model of amorphous materials

We present a two-dimensional mesoscopic model of a yield stress material that includes the possibility of local volume fluctuations coupled to shear, in such a way that the shear strength of the material decreases as the local density decreases. The model reproduces a number of effects well known in the phenomenology of this kind of materials. Particularly, we find that: the volume of the sample increases as the deformation rate increases; shear bands are no longer oriented at 45 $^\circ$ with respect to the principal axis of the applied stress (as in the absence of volume-shear coupling); homogeneous deformation becomes unstable at low enough deformation rates if volume-shear coupling is strong enough. We also analyze the implications of this coupling in the context of out of equilibrium shear bands appearing for instance in metallic glasses.