34,197 research outputs found
Continuum approach to wide shear zones in quasi-static granular matter
Slow and dense granular flows often exhibit narrow shear bands, making them
ill-suited for a continuum description. However, smooth granular flows have
been shown to occur in specific geometries such as linear shear in the absence
of gravity, slow inclined plane flows and, recently, flows in split-bottom
Couette geometries. The wide shear regions in these systems should be amenable
to a continuum description, and the theoretical challenge lies in finding
constitutive relations between the internal stresses and the flow field. We
propose a set of testable constitutive assumptions, including
rate-independence, and investigate the additional restrictions on the
constitutive relations imposed by the flow geometries. The wide shear layers in
the highly symmetric linear shear and inclined plane flows are consistent with
the simple constitutive assumption that, in analogy with solid friction, the
effective-friction coefficient (ratio between shear and normal stresses) is a
constant. However, this standard picture of granular flows is shown to be
inconsistent with flows in the less symmetric split-bottom geometry - here the
effective friction coefficient must vary throughout the shear zone, or else the
shear zone localizes. We suggest that a subtle dependence of the
effective-friction coefficient on the orientation of the sliding layers with
respect to the bulk force is crucial for the understanding of slow granular
flows.Comment: 11 pages, 7 figure
Quasistatic rheology and the origins of strain
Features of rheological laws applied to solid-like granular materials are
recalled and confronted to microscopic approaches via discrete numerical
simulations. We give examples of model systems with very similar equilibrium
stress transport properties -- the much-studied force chains and force
distribution -- but qualitatively different strain responses to stress
increments. Results on the stability of elastoplastic contact networks lead to
the definition of two different rheological regimes, according to whether a
macroscopic fragility property (propensity to rearrange under arbitrary small
stress increments in the thermodynamic limit) applies. Possible consequences
are discussed.Comment: Published in special issue of "Comptes-Rendus Physique" on granular
material
Soft grain compression: beyond the jamming point
We present the experimental studies of highly strained soft bidisperse
granular systems made of hyperelastic and plastic particles. We explore the
behavior of granular matter deep in the jammed state from local field
measurement from the grain scale to the global scale. By mean of digital image
correlation and accurate image recording we measure for each compression step
the evolution of the particle geometries and their right Cauchy-Green strain
tensor fields. We analyze the evolution of the usual macroscopic observables
(stress, packing fraction, coordination, fraction of non-rattlers,
\textit{etc}.) along the compression process through the jamming point and far
beyond. We also analyze the evolution of the local strain statistics and
evidence a crossover in the material behavior deep in the jammed state. We show
that this crossover depends on the particle material. We argue that the strain
field is a reliable observable to describe the evolution of a granular system
through the jamming transition and deep in the dense packing state whatever is
the material behavior.Comment: 10 figure
How granular materials deform in quasistatic conditions
Based on numerical simulations of quasistatic deformation of model granular
materials, two rheological regimes are distinguished, according to whether
macroscopic strains merely reflect microscopic material strains within the
grains in their contact regions (type I strains), or result from instabilities
and contact network rearrangements at the microscopic level (type II strains).
We discuss the occurrence of regimes I and II in simulations of model materials
made of disks (2D) or spheres (3D). The transition from regime I to regime II
in monotonic tests such as triaxial compression is different from both the
elastic limit and from the yield threshold. The distinction between both types
of response is shown to be crucial for the sensitivity to contact-level
mechanics, the relevant variables and scales to be considered in
micromechanical approaches, the energy balance and the possible occurrence of
macroscopic instabilitie
A stochastic flow rule for granular materials
There have been many attempts to derive continuum models for dense granular
flow, but a general theory is still lacking. Here, we start with Mohr-Coulomb
plasticity for quasi-2D granular materials to calculate (average) stresses and
slip planes, but we propose a "stochastic flow rule" (SFR) to replace the
principle of coaxiality in classical plasticity. The SFR takes into account two
crucial features of granular materials - discreteness and randomness - via
diffusing "spots" of local fluidization, which act as carriers of plasticity.
We postulate that spots perform random walks biased along slip-lines with a
drift direction determined by the stress imbalance upon a local switch from
static to dynamic friction. In the continuum limit (based on a Fokker-Planck
equation for the spot concentration), this simple model is able to predict a
variety of granular flow profiles in flat-bottom silos, annular Couette cells,
flowing heaps, and plate-dragging experiments -- with essentially no fitting
parameters -- although it is only expected to function where material is at
incipient failure and slip-lines are inadmissible. For special cases of
admissible slip-lines, such as plate dragging under a heavy load or flow down
an inclined plane, we postulate a transition to rate-dependent Bagnold
rheology, where flow occurs by sliding shear planes. With different yield
criteria, the SFR provides a general framework for multiscale modeling of
plasticity in amorphous materials, cycling between continuum limit-state stress
calculations, meso-scale spot random walks, and microscopic particle
relaxation
Demonstration of dispersive rarefaction shocks in hollow elliptical cylinder chains
We report an experimental and numerical demonstration of dispersive
rarefaction shocks (DRS) in a 3D-printed soft chain of hollow elliptical
cylinders. We find that, in contrast to conventional nonlinear waves, these DRS
have their lower amplitude components travel faster, while the higher amplitude
ones propagate slower. This results in the backward-tilted shape of the front
of the wave (the rarefaction segment) and the breakage of wave tails into a
modulated waveform (the dispersive shock segment). Examining the DRS under
various impact conditions, we find the counter-intuitive feature that the
higher striker velocity causes the slower propagation of the DRS. These unique
features can be useful for mitigating impact controllably and efficiently
without relying on material damping or plasticity effects
Solid behavior of anisotropic rigid frictionless bead assemblies
We investigate the structure and mechanical behavior of assemblies of
frictionless, nearly rigid equal-sized beads, in the quasistatic limit, by
numerical simulation. Three different loading paths are explored: triaxial
compression, triaxial extension and simple shear. Generalizing recent results
[1], we show that the material, despite rather strong finite sample size
effects, is able to sustain a finite deviator stress in the macroscopic limit,
along all three paths, without dilatancy. The shape of the yield surface is
adequately described by a Lade-Duncan (rather than Mohr-Coulomb) criterion.
While scalar state variables keep the same values as in isotropic systems,
fabric and force anisotropies are each characterized by one parameter and are
in one-to-one correspondence with principal stress ratio along all three
loading paths.The anisotropy of the pair correlation function extends to a
distance between bead surfaces on the order of 10% of the diameter. The tensor
of elastic moduli is shown to possess a nearly singular, uniaxial structure
related to stress anisotropy. Possible stress-strain relations in monotonic
loading paths are also discussed
Highly nonlinear solitary waves in chains of ellipsoidal particles
We study the dynamic response of a one-dimensional chain of ellipsoidal particles excited by a single compressive impulse. We detail the Hertzian contact theory describing the interaction between two ellipsoidal particles under compression, and use it to model the dynamic response of the system. We observe the formation of highly nonlinear solitary waves in the chain, and we also study their propagation properties. We measure experimentally the traveling pulse amplitude (force), the solitary wave speed, and the solitary wave width. We compare these results with theoretical predictions in the long wavelength approximation, and with numerical results obtained with a discrete particle model and with finite element simulations. We also study the propagation of highly nonlinear solitary waves in the chain with particles arranged in different configurations to show the effects of the particle's geometry on the wave propagation characteristics and dissipation. We find very good agreement between experiment, theory, and simulations for all the ranges of impact velocity and particle arrangements investigated
Micromechanical analysis of kinematic hardening in natural clay
This paper presents a micromechanical analysis of the macroscopic behaviour of natural clay. A microstructural stress-strain model for clayey material has been developed which considers clay as a collection of clusters. The deformation of a representative volume of the material is generated by mobilizing and compressing all the clusters along their contact planes. Numerical simulations of multistage drained triaxial stress paths on Otaniemi clay have been performed and compared the numerical results to the experimental ones in order to validate the modelling approach. Then, the numerical results obtained at the microscopic level were analysed in order to explain the induced anisotropy observed in the clay behaviour at the macroscopic level. The evolution of the state variables at each contact plane during loading can explain the changes in shape and position in the stress space of the yield surface at the macroscopic level, as well as the rotation of the axes of anisotropy of the material
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