18 research outputs found
Fluid-solid transition in unsteady, homogeneous, granular shear flows
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.Comment: 20 pages, 14 figures, submitted to Granular Matte
Plane shear flows of frictionless spheres: Kinetic theory and 3D soft-sphere discrete element method simulations
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
Merging fluid and solid granular behavior
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 Matte
Fluid-solid transition in unsteady shearing flows
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
Plane shear flows of frictionless spheres: kinetic theory and 3D soft-sphere discrete element method simulations
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
Granular Flow: From Dilute to Jammed States
Particulate systems and granular matter display dynamic or static, fluidâ or solidâlike states, respectively, or both at the same time. The mystery of bridging the gap between the particulate, microscopic state and the macroscopic, continuum description is one of the challenges of modern research. This book chapter gives an overview of recent progress and some new insights about the collective mechanical behavior of granular, deformable particles
Shearing flows of frictionless spheres over bumpy planes: slip velocity
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 bumpinessâ\u80\u94small distance between the wall-particlesâ\u80\u94the 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