80 research outputs found
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
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
Geometric origin of mechanical properties of granular materials
Some remarkable generic properties, related to isostaticity and potential
energy minimization, of equilibrium configurations of assemblies of rigid,
frictionless grains are studied. Isostaticity -the uniqueness of the forces,
once the list of contacts is known- is established in a quite general context,
and the important distinction between isostatic problems under given external
loads and isostatic (rigid) structures is presented. Complete rigidity is only
guaranteed, on stability grounds, in the case of spherical cohesionless grains.
Otherwise, the network of contacts might deform elastically in response to load
increments, even though grains are rigid. This sets an uuper bound on the
contact coordination number. The approximation of small displacements (ASD)
allows to draw analogies with other model systems studied in statistical
mechanics, such as minimum paths on a lattice. It also entails the uniqueness
of the equilibrium state (the list of contacts itself is geometrically
determined) for cohesionless grains, and thus the absence of plastic
dissipation. Plasticity and hysteresis are due to the lack of such uniqueness
and may stem, apart from intergranular friction, from small, but finite,
rearrangements, in which the system jumps between two distinct potential energy
minima, or from bounded tensile contact forces. The response to load increments
is discussed. On the basis of past numerical studies, we argue that, if the ASD
is valid, the macroscopic displacement field is the solution to an elliptic
boundary value problem (akin to the Stokes problem).Comment: RevTex, 40 pages, 26 figures. Close to published paper. Misprints and
minor errors correcte
Stylolites, porosity, depositional texture, and silicates in chalk facies sediments:Ontong Java Plateau - Gorm and Tyra fields, North Sea
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