7,176 research outputs found
Internal states of model isotropic granular packings. II. Compression and pressure cycles
This is the second paper of a series of three investigating, by numerical
means, the geometric and mechanical properties of spherical bead packings under
isotropic stresses. We study the effects of varying the applied pressure P
(from 1 or 10 kPa up to 100 MPa in the case of glass beads) on several types of
configurations assembled by different procedures, as reported in the preceding
paper. As functions of P, we monitor changes in solid fraction \Phi,
coordination number z, proportion of rattlers (grains carrying no force) x0,
the distribution of normal forces, the level of friction mobilization, and the
distribution of near neighbor distances. Assuming the contact law does not
involve material plasticity or damage, \Phi is found to vary very nearly
reversibly with P in an isotropic compression cycle, but all other quantities,
due to the frictional hysteresis of contact forces, change irreversibly. In
particular, initial low P states with high coordination numbers lose many
contacts in a compression cycle, and end up with values of z and x0 close to
those of the most poorly coordinated initial configurations. Proportional load
variations which do not entail notable configuration changes can therefore
nevertheless significantly affect contact networks of granular packings in
quasistatic conditions.Comment: Published in Physical Review E 12 page
Experimental evidence of ageing and slow restoration of the weak-contact configuration in tilted 3D granular packings
Granular packings slowly driven towards their instability threshold are
studied using a digital imaging technique as well as a nonlinear acoustic
method. The former method allows us to study grain rearrangements on the
surface during the tilting and the latter enables to selectively probe the
modifications of the weak-contact fraction in the material bulk. Gradual ageing
of both the surface activity and the weak-contact reconfigurations is observed
as a result of repeated tilt cycles up to a given angle smaller than the angle
of avalanche. For an aged configuration reached after several consecutive tilt
cycles, abrupt resumption of the on-surface activity and of the weak-contact
rearrangements occurs when the packing is subsequently inclined beyond the
previous maximal tilting angle. This behavior is compared with literature
results from numerical simulations of inclined 2D packings. It is also found
that the aged weak-contact configurations exhibit spontaneous restoration
towards the initial state if the packing remains at rest for tens of minutes.
When the packing is titled forth and back between zero and near-critical
angles, instead of ageing, the weak-contact configuration exhibits "internal
weak-contact avalanches" in the vicinity of both the near-critical and zero
angles. By contrast, the stronger-contact skeleton remains stable
Geometrical families of mechanically stable granular packings
We enumerate and classify nearly all of the possible mechanically stable (MS)
packings of bidipserse mixtures of frictionless disks in small sheared systems.
We find that MS packings form continuous geometrical families, where each
family is defined by its particular network of particle contacts. We also
monitor the dynamics of MS packings along geometrical families by applying
quasistatic simple shear strain at zero pressure. For small numbers of
particles (N < 16), we find that the dynamics is deterministic and highly
contracting. That is, if the system is initialized in a MS packing at a given
shear strain, it will quickly lock into a periodic orbit at subsequent shear
strain, and therefore sample only a very small fraction of the possible MS
packings in steady state. In studies with N>16, we observe an increase in the
period and random splittings of the trajectories caused by bifurcations in
configuration space. We argue that the ratio of the splitting and contraction
rates in large systems will determine the distribution of MS-packing
geometrical families visited in steady-state. This work is part of our
long-term research program to develop a master-equation formalism to describe
macroscopic slowly driven granular systems in terms of collections of small
subsystems.Comment: 18 pages, 23 figures, 5 table
The Galois Complexity of Graph Drawing: Why Numerical Solutions are Ubiquitous for Force-Directed, Spectral, and Circle Packing Drawings
Many well-known graph drawing techniques, including force directed drawings,
spectral graph layouts, multidimensional scaling, and circle packings, have
algebraic formulations. However, practical methods for producing such drawings
ubiquitously use iterative numerical approximations rather than constructing
and then solving algebraic expressions representing their exact solutions. To
explain this phenomenon, we use Galois theory to show that many variants of
these problems have solutions that cannot be expressed by nested radicals or
nested roots of low-degree polynomials. Hence, such solutions cannot be
computed exactly even in extended computational models that include such
operations.Comment: Graph Drawing 201
- …