Rheology of granular flows across the transition from soft to rigid particles

The rheology of dense granular flows is often seen as dependent on the nature of the energy landscape defining the modes of energy relaxation under shear. We investigate numerically the transition from soft to rigid particles, varying $S$, their stiffness compared to the confining pressure over three decades and the inertial number $I$ of the shear flow over five decades. We show that the rheological constitutive relation, characterized by a dynamical friction coefficient of the form $\mu(I)=\mu_c + a I^{\alpha}$ is marginally affected by the particle stiffness, with constitutive parameters being essentially dependent on the inter-particle friction. Similarly, the distribution of local shear rate mostly depends on the inertial number $I$, which shows that the characteristic timescale of plastic events is primarily controlled by the confining pressure and is insensitive to $S$. By contrast, the form under which energy is stored between these events, but also the contact network properties such as the coordination number and the distance to isostaticity, are strongly affected by stiffness, allowing us to discuss the different regimes in the $(S,I)$ phase space.