Fluid-solid transition in unsteady, homogeneous, granular shear flows

Abstract: Discrete element numerical simulations of unsteady, homogeneous shear flows have been performed by instantly applying a constant shear rate to a random, static, isotropic assembly of identical, soft, frictional spheres at either zero or finite pressure by keeping constant the solid volume fraction until the steady state is reached. If the system is slowly sheared, or, equivalently, if the particles are sufficiently rigid, the granular material exhibits either large or small fluctuations in the evolving pressure, depending whether the average number of contacts per particle (coordination number) is less or larger than a critical value. The amplitude of the pressure fluctuations is rate-dependent when the coordination number is less than the critical and rate-independent otherwise, signatures of fluid-like and solid-like behaviour, respectively. The same critical coordination number has been previously found to represent the minimum value at which rate-independent components of the stresses develop in steady, simple shearing and the jamming transition in isotropic random packings. The observed complex behaviour of the measured pressure in the fluid-solid transition clearly suggests the need for incorporating in a nontrivial way the coordination number, the solid volume fraction, the particle stiffness and the intensity of the particle agitation in constitutive models for the onset and the arrest of granular flows.