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 material. In particular, we find that the volume of the sample increases as the deformation rate increases; shear bands are no longer oriented at 45^{∘} with respect to the principal axis of the applied stress (as in the absence of volume-shear coupling); and homogeneous deformation becomes unstable at low enough deformation rates if volume-shear coupling is strong enough. We also discuss the effect of this coupling on some out-of-equilibrium configurations, which can be relevant to the study of the shear bands observed in metallic glasses.