  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.
