238 research outputs found
Micromechanical study of elastic moduli of loose granular materials
In micromechanics of the elastic behaviour of granular materials, the macro-scale continuum elastic moduli are expressed in terms of micro-scale parameters, such as coordination number (the average number of contacts per particle) and interparticle contact stiffnesses in normal and tangential directions. It is well-known that mean-field theory gives inaccurate micromechanical predictions of the elastic moduli, especially for loose systems with low coordination number. Improved predictions of the moduli are obtained here for loose two-dimensional, isotropic assemblies. This is achieved by determining approximate displacement and rotation fields from the force and moment equilibrium conditions for small sub-assemblies of various sizes. It is assumed that the outer particles of these sub-assemblies move according to the mean field. From the particle displacement and rotation fields thus obtained, approximate elastic moduli are determined. The resulting predictions are compared with the true moduli, as determined from the discrete element method simulations for low coordination numbers and for various values of the tangential stiffness (at fixed value of the normal stiffness). Using this approach, accurate predictions of the moduli are obtained, especially when larger sub-assemblies are considered. As a step towards an analytical formulation of the present approach, it is investigated whether it is possible to replace the local contact stiffness matrices by a suitable average stiffness matrix. It is found that this generally leads to a deterioration of the accuracy of the predictions. Many micromechanical studies predict that the macroscopic bulk modulus is hardly influenced by the value of the tangential stiffness. It is shown here from the discrete element method simulations of hydrostatic compression that for loose systems, the bulk modulus strongly depends on the stiffness ratio for small stiffness ratios
Long Range Correlation in Granular Shear Flow II: Theoretical Implications
Numerical simulations are used to test the kinetic theory constitutive
relations of inertial granular shear flow. These predictions are shown to be
accurate in the dilute regime, where only binary collisions are relevant, but
underestimate the measured value in the dense regime, where force networks of
size are present. The discrepancy in the dense regime is due to
non-collisional forces that we measure directly in our simulations and arise
from elastic deformations of the force networks. We model the non-collisional
stress by summing over all paths that elastic waves travel through force
networks. This results in an analytical theory that successfully predicts the
stress tensor over the entire inertial regime without any adjustable
parameters
Multiscale Analysis of the Stress State in a Granular Slope in Transition to Failure
By means of contact dynamics simulations, we analyze the stress state in a
granular bed slowly tilted towards its angle of repose. An increasingly large
number of grains are overloaded in the sense that they are found to carry a
stress ratio above the Coulomb yield threshold of the whole packing. Using this
property, we introduce a coarse-graining length scale at which all stress
ratios are below the packing yield threshold. We show that this length
increases with the slope angle and jumps to a length comparable to the depth of
the granular bed at an angle below the angle of repose. This transition
coincides with the onset of dilatation in the packing. We map this transition
into a percolation transition of the overloaded grains, and we argue that in
the presence of long-range correlations above the transition angle, the
granular slope is metastable.Comment: 11 pages, 14 Fig, submitted to PR
Discrete element modelling of creep of asphalt mixtures
Creep tests on asphalt mixtures have been undertaken under four stress levels in the laboratory while the Discrete Element Model (DEM) has been used to simulate the laboratory tests. A modified Burger’s model has been used to represent the time-dependent behaviour of an asphalt mixture by adding time-dependent moment and torsional resistance at contacts. Parameters were chosen to give the correct stress-strain response for constant strain rate tests in Cai et al. (2013) . The stress-strain response for the laboratory creep tests and the simulations were recorded. The DEM results show reasonable agreement with the experiments. The creep simulation results proved to be dependent on both bond strength variability and positions of the particles. Bond breakage was recorded during the simulations and used to investigate the micro-mechanical deformation behaviour of the asphalt mixtures. An approach based on dimensional analysis is also presented in this paper to reduce the computational time during the creep simulation, and this analysis is also a new contribution
Stress-strain behavior and geometrical properties of packings of elongated particles
We present a numerical analysis of the effect of particle elongation on the
quasistatic behavior of sheared granular media by means of the Contact Dynamics
method. The particle shapes are rounded-cap rectangles characterized by their
elongation. The macroscopic and microstructural properties of several packings
subjected to biaxial compression are analyzed as a function of particle
elongation. We find that the shear strength is an increasing linear function of
elongation. Performing an additive decomposition of the stress tensor based on
a harmonic approximation of the angular dependence of branch vectors, contact
normals and forces, we show that the increasing mobilization of friction force
and the associated anisotropy are key effects of particle elongation. These
effects are correlated with partial nematic ordering of the particles which
tend to be oriented perpendicular to the major principal stress direction and
form side-to-side contacts. However, the force transmission is found to be
mainly guided by cap-to-side contacts, which represent the largest fraction of
contacts for the most elongated particles. Another interesting finding is that,
in contrast to shear strength, the solid fraction first increases with particle
elongation, but declines as the particles become more elongated. It is also
remarkable that the coordination number does not follow this trend so that the
packings of more elongated particles are looser but more strongly connected.Comment: Submited to Physical Review
Unilateral interactions in granular packings: A model for the anisotropy modulus
Unilateral interparticle interactions have an effect on the elastic response
of granular materials due to the opening and closing of contacts during
quasi-static shear deformations. A simplified model is presented, for which
constitutive relations can be derived. For biaxial deformations the elastic
behavior in this model involves three independent elastic moduli: bulk, shear,
and anisotropy modulus. The bulk and the shear modulus, when scaled by the
contact density, are independent of the deformation. However, the magnitude of
the anisotropy modulus is proportional to the ratio between shear and
volumetric strain. Sufficiently far from the jamming transition, when
corrections due to non-affine motion become weak, the theoretical predictions
are qualitatively in agreement with simulation results.Comment: 6 pages, 5 figure
Force transmission in a packing of pentagonal particles
We perform a detailed analysis of the contact force network in a dense
confined packing of pentagonal particles simulated by means of the contact
dynamics method. The effect of particle shape is evidenced by comparing the
data from pentagon packing and from a packing with identical characteristics
except for the circular shape of the particles. A counterintuitive finding of
this work is that, under steady shearing, the pentagon packing develops a lower
structural anisotropy than the disk packing. We show that this weakness is
compensated by a higher force anisotropy, leading to enhanced shear strength of
the pentagon packing. We revisit "strong" and "weak" force networks in the
pentagon packing, but our simulation data provide also evidence for a large
class of "very weak" forces carried mainly by vertex-to-edge contacts. The
strong force chains are mostly composed of edge-to-edge contacts with a marked
zig-zag aspect and a decreasing exponential probability distribution as in a
disk packing
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
- …