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This work focuses on the behaviour of granular materials under unsteady, simple shear conditions and, in particular, on from solid- to fluid-like phase transition. The authors introduce a theoretical model, based on continuum mechanics, able of predicting the mechanical behaviour of granular media under both quasi-static and dynamic conditions. The model assumes a parallel scheme where confining and shear stresses are computed as the sum of two contributions: the quasi-static and the collisional one. The quasi-static contribution is obtained by employing an elastic–plastic model including the critical state concept, while the collisional one is derived from the kinetic theory of granular gases. In order to test the model under unsteady conditions, DEM numerical simulations of time evolving homogeneous shear flows have been performed by considering an assembly of frictional, deformable spheres, under constant volume conditions. Simulations have been performed by systematically changing both void ratio and shear rate. The comparison between theoretical model predictions and DEM results is done in terms of time evolution of stresses and granular temperature. Suitable initial conditions are imposed to reproduce both solid to fluid (liquefaction) and fluid to solid (solidification) phase transitions.

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.

In this paper, the authors analyse numerical and experimental results concerning either dry or saturated granular flows under steady, simple shear conditions. A new constitutive model is introduced, on the base of the mixture theory, according to which granular and liquid phases are considered separately. The constitutive relationship refers to the representative elementary volume and assumes that the mean values of all kinematic variables, of both granular and liquid phases, coincide. For the two phases, a parallel scheme is chosen. As regards the granular contribution, the authors employ an already conceived constitutive model where the critical state concept and the kinetic theory of granular gases are merged, and in which the granular temperature plays the role of state variable for the material. Under saturated conditions, the new model accounts for granular–liquid coupling effects. In fact, the liquid viscosity is a function of granular concentration, whereas the evolution of granular temperature is influenced by the liquid molecular viscosity. The model is validated against numerical results and critically discussed. For sufficiently small values of concentration, the transition from a Newtonian to a Bagnoldian regime, for increasing values of strain rate, is correctly reproduced.

Simple homogeneous shear flows of frictionless, deformable particles are studied by particle simulations at large shear rates and for differently soft, deformable particles. The particle stiffness sets a time-scale that can be used to scale the physical quantities; thus the dimensionless shear rate, i.e. the inertial number (inversely proportional to pressure), can alternatively be expressed as inversely proportional to the square root of the particle stiffness. Asymptotic scaling relations for the field variables pressure, shear stress and granular temperature are inferred from simulations in both fluid and solid regimes, corresponding to unjammed and jammed conditions. Then the limit cases are merged to unique constitutive relations that cover also the transition zone in proximity of jamming. By exploiting the diverging behavior of the scaling laws at the jamming density, we arrive at continuous and differentiable phenomenological constitutive relations for the stresses and the granular temperature as functions of the volume fraction, shear rate, particle stiffness and distance from jamming. In contrast to steady shear flows of hard particles the (shear) stress ratio does not collapse as a function of the inertial number, indicating the need for an additional control parameter. In the range of particle stiffnesses investigated, in the solid regime, only the pressure is rate independent, whereas the shear stress exhibits a slight shear rate- and stiffness-dependency., Comment: 37 pages, 14 figures, submitted to Soft Matter

Boundary conditions for the slip velocity of inelastic, frictionless spheres interacting with bumpy walls are derived via discrete element method simulations of Couette granular flows. The bumpiness is created by gluing spheres identical to those flowing in a regular hexagonal array to a flat plane. Depending on the particle inelasticity and bumpiness, the characteristics of the flow range from simple shearing to plug flow. At low bumpiness—small distance between the wall-particles—the ratio of particle shear stress to pressure is a non-linear function of the slip velocity and presents a maximum. At high bumpiness, the bumpy plane behaves as a flat, frictional surface and the stress ratio saturates to a constant value for large slip velocity.

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.

The numerical simulation of rapid landslides is quite complex mainly because constitutive models capable of simulating the mechanical behaviour of granular materials in the pre-collapse and post-collapse regimes are still missing. The goal of this paper is to introduce a constitutive model capable of capturing the response of dry granular flows from quasi-static to dynamic conditions, in particular when the material experiences a sort of solid-to-fluid phase transition. An ideal assembly of identical spheres under simple shear conditions is considered. In the constitutive model, void ratio and granular temperature have been chosen as state variables, and both shear and normal stresses are computed as the sum of two contributions: the quasi-static one and the collisional one. The former is determined by using a perfect elasto-plastic model including the critical state concept, while the latter is derived from the kinetic theory of granular gases. The evolution of the granular temperature, fundamentally governing the material phase transition, is obtained by imposing the kinetic fluctuating energy balance. The constitutive relationship has been integrated, under both constant pressure and constant volume conditions, and the influence of shear strain rate, initial void ratio and normal pressure on the mechanical response has been investigated.

We use previous results from discrete element simulations of simple shear flows of rigid, identical spheres in the collisional regime to show that the volume fractiondependence of the stresses is singular at the shear rigidity. Here, we identify the shear rigidity, which is a decreasing function of the interparticle friction, as the maximum volume fraction beyond which a random collisional assembly of grains cannot be sheared without developing force chains that span the entire domain. In the framework of extended kinetic theory, i.e., kinetic theory that accounts for the decreasing in the collisional dissipation due to the breaking of molecular chaos at volume fractions larger than 0.49, we also show that the volume fraction-dependence of the correlation length (measure of the velocity correlation) is singular at random close packing, independent of the interparticle friction. The difference in the singularities ensures that the ratio of the shear stress to the pressure at shear rigidity is different from zero even in the case of frictionless spheres: we identify that with the yield stress ratio of granular materials, and we show that the theoretical predictions, once the different singularities are inserted into the functions of extended kinetic theory, are in excellent agreement with the results of numerical simulations.

This paper focuses on the mechanical behaviour of granular systems under shearing, unsteady conditions. The results of numerical simulations of time evolving, homogeneous, shear flows of an assembly of frictional spheres, under constant volume conditions are illustrated. Simulations have been performed considering three volume fractions corresponding to fluid, solid and near-to-critical conditions at steady state. The three systems follow very different evolutionary paths, in terms of pressure, coordination number and stress ratio. Fluid-like and solid-like systems exhibit large and small fluctuations, respectively, in those quantities. A critical value of the coordination number seems to govern the transition from fluid to solid.

SUMMARY This paper aims at extending the well-known critical state concept, associated with quasi-static conditions, by accounting for the role played by the strain rate when focusing on the steady, simple shear flow of a dry assembly of identical, inelastic, soft spheres. An additional state variable for the system, the granular temperature, is accounted for. The granular temperature is related to the particle velocity fluctuations and measures the agitation of the system. This state variable, as is in the context of kinetic theories of granular gases, is assumed to govern the response of the material at large strain rates and low concentrations. The stresses of the system are associated with enduring, frictional contacts among particles involved in force chains and nearly instantaneous collisions. When the first mechanism prevails, the material behaves like a solid, and constitutive models of soil mechanics hold, whereas when inelastic collisions dominate, the material flows like a granular gas, and kinetic theories apply. Considering a pressure-imposed flow, at large values of the normal stress and small values of the shear rate, the theory predicts a nonmonotonic shear rate dependence of the stress ratio at the steady state, which is likely to govern the evolution of landslides. Copyright © 2013 John Wiley & Sons, Ltd.

International audience; We use existing 3D Discrete Element simulations of simple shear flows of spheres to evaluate the radial distribution function at contact that enables kinetic theory to correctly predict the pressure and the shear stress, for different values of the collisional coefficient of restitution. Then, we perform 3D Discrete Element simulations of plane flows of frictionless, inelastic spheres, sheared between walls made bumpy by gluing particles in a regular array, at fixed average volume fraction and distance between the walls. The results of the numerical simulations are used to derive boundary conditions appropriated in the cases of large and small bumpiness. Those boundary conditions are, then, employed to numerically integrate the differential equations of Extended Kinetic Theory, where the breaking of the molecular chaos assumption at volume fraction larger than 0.49 is taken into account in the expression of the dissipation rate. We show that the Extended Kinetic Theory is in very good agreement with the numerical simulations, even for coefficients of restitution as low as 0.50. When the bumpiness is increased, we observe that some of the flowing particles are stuck in the gaps between the wall spheres. As a consequence, the walls are more dissipative than expected, and the flows resemble simple shear flows, i.e., flows of rather constant volume fraction and granular temperature.

This work focuses on the mechanical response of dry granular materials under steady, simple shear conditions. In particular, the goal is to obtain a complete rheology able to describe the material behavior within the entire range of concentrations for which the flow can be considered dense. The total stress is assumed to be the linear sum of a frictional and a kinetic component. The frictional and the kinetic contributions are modeled in the context of the critical state theory and the kinetic theory of dense granular gases, respectively; in the latter, the correlated motion among the particles, which is likely to occur at high concentration, is also included. In accordance with recent findings on disordered granular packings, the frictional component of stresses is assumed to vanish when the concentration is below the random loose packing. According to this approach, four nondimensional quantities govern steady, simple shear flows: the concentration, the shear to normal stress ratio, the ratio of the time scales associated with the motion perpendicular and parallel to the flow, and the ratio between the particle stiffness and the normal stress. The present theory allows us to reproduce, in a notable way, both numerical simulations on simple shear flows of disks and physical experiments on incline flows of glass spheres taken from the literature.