We propose an explanation for the onset of oscillations seen in numerical simulations of dense, inclined flows of inelastic, frictional spheres. It is based on a phase transition between disordered and ordered collisional states that may be interrupt
ed by the formation of force chains. Low frequency oscillations between ordered and disordered states take place over weakly bumpy bases; higher-frequency oscillations over strongly bumpy bases involve the formation of particle chains that extend to the base and interrupt the phase change. The predicted frequency and amplitude of the oscillations induced by the unstable part of the equation of state are similar to those seen in the simulations and they depend upon the contact stiffness in the same way. Such oscillations could be the source of sound produced by flowing sand.
We test the elasticity of granular aggregates using increments of shear and volume strain in a numerical simulation. We find that the increment in volume strain is almost reversible, but the increment in shear strain is not. The strength of this irre
versibility increases as the average number of contacts per particle (the coordination number) decreases. For increments of volume strain, an elastic model that includes both average and fluctuating motions between contacting particles reproduces well the numerical results over the entire range of coordination numbers. For increments of shear strain, the theory and simulations agree quite well for high values of the coordination number.
