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We perform discrete element simulations of freely cooling, dense granular materials, previously sheared at a constant rate. Particles are identical, frictional spheres interacting via linear springs and dashpots and the solid volume fraction is constant and equal to 60% during both shearing and cooling. We measure the average and the distributions of contacts per particle and the anisotropy of the contact network. We observe that the granular material, at the beginning of cooling, can be shear-jammed, fragile or unjammed. The initial state determines the subsequent evolution of the dense assembly into either an anisotropic solid, an isotropic or an anisotropic fluid, respectively. While anisotropic solids and isotropic fluids rapidly reach an apparent final steady configuration, the microstructure continues to evolve for anisotropic fluids. We explain this with the presence of vortices in the flow field that counteract the randomizing and structure-annihilating effect of collisions. We notice, in accordance with previous findings, that the initial fraction of mechanically stable particles permits to distinguish between shear-jammed, fragile or unjammed states and, therefore, determine beforehand the fate of the freely evolving granular materials. We also find that the fraction of mechanically stable particles is in a one-to-one relation with the average number of contacts per particle. The latter is, therefore, a variable that must be incorporated in continuum models of granular materials, even in the case of unjammed states, where it was widely accepted that the solid volume fraction was sufficient to describe the geometry of the system.

Discrete element numerical simulations of unsteady, homogeneous flows have been performed by shearing a fixed volume of identical, soft, frictional spheres. A constant, global, shear rate was instantly applied to particles that are initially at rest, non interacting, and randomly distributed. 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. When the coordination number is less than the critical value, the amplitude of the pressure fluctuations is dependent on the shear rate, whereas, it is rate-independent in the opposite case, signatures, according to the case, of fluid-like and solid-like behaviour. The same critical coordination number has been previously found to represent the minimum value at which rate-independent components of 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 can be predicted with a constitutive model involving the coordination number, the particle stiffness and the intensity of particle agitation.