8,039 research outputs found
Numerical stress probing on a 2D model granular material
We use DEM simulations on a simple 2D model of a granular material to measure its deformation response to small stress increments of arbitrary directions (stress probes) and assess the applicability of the classical concepts of elastoplasticity. We impose stress increments in the space of principal stresses components, to numerical specimens selected at various intermediate states along the biaxial compression path. The elastic part of the incremental response is systematically identified by building the elastic stiffness matrix of well-equilibrated configurations. Plastic strain increments are computed standing on the partition hypothesis for strain increments into elastic- and plastic parts. The domain of validity of the partition hypothesis is discussed, playing extensively with the magnitude of the stress increments, in order to identify a range in which the incremental response is homogeneous of degree 1 and the essential features of plasticity models can be observed. We investigate in particular the existence of a plastic flow rule with a clearly defined plastic flow direction and yield criterion. The robustness of these features is tested over a range of contact stiffness levels and against the dominant deformation modes (i.e., based on contact deformation or network rearrangement)
Strain versus stress in a model granular material: a Devil's staircase
The series of equilibrium states reached by disordered packings of rigid,
frictionless discs in two dimensions, under gradually varying stress, are
studied by numerical simulations. Statistical properties of trajectories in
configuration space are found to be independent of specific assumptions ruling
granular dynamics, and determined by geometry only. A monotonic increase in
some macroscopic loading parameter causes a discrete sequence of
rearrangements. For a biaxial compression, we show that, due to the statistical
importance of such events of large magnitudes, the dependence of the resulting
strain on stress direction is a Levy flight in the thermodynamic limit.Comment: REVTeX, 4 pages, 5 included PostScript figures. New version altered
throughout text, very close to published pape
A Model for Granular Texture with Steric Exclusion
We propose a new method to characterize the geometrical texture of a granular
packing at the particle scale including the steric hindrance effect. This
method is based on the assumption of a maximum disorder (entropy) compatible
both with strain-induced anisotropy of the contact network and steric
exclusions. We show that the predicted statistics for the local configurations
is in a fairly agreement with our numerical data.Comment: 9 pages, 5 figure
The TheLMA project: Multi-GPU Implementation of the Lattice Boltzmann Method
International audienceIn this paper, we describe the implementation of a multi-graphical processing unit (GPU) fluid flow solver based on the lattice Boltzmann method (LBM). The LBM is a novel approach in computational fluid dynamics, with numerous interesting features from a computational, numerical, and physical standpoint. Our program is based on CUDA and uses POSIX threads to manage multiple computation devices. Using recently released hardware, our solver may therefore run eight GPUs in parallel, which allows us to perform simulations at a rather large scale. Performance and scalability are excellent, the speedup over sequential implementations being at least of two orders of magnitude. In addition, we discuss tiling and communication issues for present and forthcoming implementations
An algorithm to calculate the transport exponent in strip geometries
An algorithm for solving the random resistor problem by means of the
transfer-matrix approach is presented. Preconditioning by spanning clusters
extraction both reduces the size of the conductivity matrix and speed up the
calculations.Comment: 17 pages, RevTeX2.1, HLRZ - 97/9
Scattering by a toroidal coil
In this paper we consider the Schr\"odinger operator in with
a long-range magnetic potential associated to a magnetic field supported inside
a torus . Using the scheme of smooth perturbations we construct
stationary modified wave operators and the corresponding scattering matrix
. We prove that the essential spectrum of is an
interval of the unit circle depending only on the magnetic flux across
the section of . Additionally we show that, in contrast to the
Aharonov-Bohm potential in , the total scattering cross-section
is always finite. We also conjecture that the case treated here is a typical
example in dimension 3.Comment: LaTeX2e 17 pages, 1 figur
Internal states of model isotropic granular packings. I. Assembling process, geometry and contact networks
This is the first paper of a series of three, reporting on numerical
simulation studies of geometric and mechanical properties of static assemblies
of spherical beads under an isotropic pressure. Frictionless systems assemble
in the unique random close packing (RCP) state in the low pressure limit if the
compression process is fast enough, slower processes inducing traces of
crystallization, and exhibit specific properties directly related to
isostaticity of the force-carrying structure. The different structures of
frictional packings assembled by various methods cannot be classified by the
sole density. While lubricated systems approach RCP densities and coordination
number z^*~=6 on the backbone in the rigid limit, an idealized "vibration"
procedure results in equally dense configurations with z^*~=4.5. Near neighbor
correlations on various scales are computed and compared to available
laboratory data, although z^* values remain experimentally inaccessible. Low
coordination packings have many rattlers (more than 10% of the grains carry no
force), which should be accounted for on studying position correlations, and a
small proportion of harmless "floppy modes" associated with divalent grains.
Frictional packings, however slowly assembled under low pressure, retain a
finite level of force indeterminacy, except in the limit of infinite friction.Comment: 29 pages. Published in Physical Review
Internal states of model isotropic granular packings. III. Elastic properties
In this third and final paper of a series, elastic properties of numerically
simulated isotropic packings of spherical beads assembled by different
procedures and subjected to a varying confining pressure P are investigated. In
addition P, which determines the stiffness of contacts by Hertz's law, elastic
moduli are chiefly sensitive to the coordination number, the possible values of
which are not necessarily correlated with the density. Comparisons of numerical
and experimental results for glass beads in the 10kPa-10MPa range reveal
similar differences between dry samples compacted by vibrations and lubricated
packings. The greater stiffness of the latter, in spite of their lower density,
can hence be attributed to a larger coordination number. Voigt and Reuss bounds
bracket bulk modulus B accurately, but simple estimation schemes fail for shear
modulus G, especially in poorly coordinated configurations under low P.
Tenuous, fragile networks respond differently to changes in load direction, as
compared to load intensity. The shear modulus, in poorly coordinated packings,
tends to vary proportionally to the degree of force indeterminacy per unit
volume. The elastic range extends to small strain intervals, in agreement with
experimental observations. The origins of nonelastic response are discussed. We
conclude that elastic moduli provide access to mechanically important
information about coordination numbers, which escape direct measurement
techniques, and indicate further perspectives.Comment: Published in Physical Review E 25 page
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