CiteULike: norris's granular

On incremental non-linearity in granular media: phenomenological and multi-scale views (Part I)

Félix Darve — 2007-02-15T16:40:06-00:00

International Journal for Numerical and Analytical Methods in Geomechanics, Vol. 29, No. 14. (2005), pp. 1387-1409.

On the basis of fundamental constitutive laws such as elasticity, perfect plasticity, and pure viscosity, many elasto-viscoplastic constitutive relations have been developed since the 1970s through phenomenological approaches. In addition, a few more recent micro-mechanical models based on multi-scale approaches are now able to describe the main macroscopic features of the mechanical behaviour of granular media. The purpose of this paper is to compare a phenomenological constitutive relation and a micro-mechanical model with respect to a basic issue regularly raised about granular assemblies: the incrementally non-linear character of their behaviour. It is shown that both phenomenological and micro-mechanical models exhibit an incremental non-linearity. In addition, the multi-scale approach reveals that the macroscopic incremental non-linearity could stem from the change in the regime of local contacts between particles (from plastic regime to elastic regime) in terms of the incremental macroscopic loading direction. Copyright © 2005 John Wiley & Sons, Ltd.

On flow rule in granular media: phenomenological and multi-scale views (Part II)

Félix Darve — 2007-02-15T16:36:54-00:00

International Journal for Numerical and Analytical Methods in Geomechanics, Vol. 29, No. 14. (2005), pp. 1411-1432.

In the companion paper (Int. J. Numer. Anal. Methods Geomech. 2005, this issue), we investigated an outstanding feature of the mechanical behaviour of granular assemblies, namely their incrementally non-linear character. For this purpose, two types of constitutive models were considered: a phenomenological model and a micro-mechanical model. The purpose of the present paper is to compare these two models with respect to another basic issue regularly raised about granular assemblies: the possible existence of a regular flow rule. This comparison brings out the essential micro-mechanical origins of singular flow rules. As a consequence of the frictional model used to describe the sliding between adjoining granules, a flow rule only exists in two-dimensional conditions, but disappears in three dimensions. Copyright © 2005 John Wiley & Sons, Ltd.

Fluctuations of acoustic field in a granular medium

ED Bazhenova — 2007-02-15T16:06:39-00:00

Acoustical Physics, Vol. V51, No. 0. (6 December 2005), pp. S37-S42.

Three wave mixing test of hyperelasticity in highly nonlinear solids: sedimentary rocks

RM D’angelo — 2007-02-15T15:18:57-00:00

JASA

Granular packings: Nonlinear elasticity, sound propagation, and collective relaxation dynamics

Hernan Makse — 2007-02-15T15:14:34-00:00

Physical Review E (Statistical, Nonlinear, and Soft Matter Physics), Vol. 70, No. 6. (2004)

Experiments on isotropic compression of a granular assembly of spheres show that the shear and bulk moduli vary with the confining pressure faster than the 1/3 power law predicted by Hertz-Mindlin effective medium theories of contact elasticity. Moreover, the ratio between the moduli is found to be larger than the prediction of the elastic theory by a constant value. The understanding of these discrepancies has been a long-standing question in the field of granular matter. Here we perform a test of the applicability of elasticity theory to granular materials. We perform sound propagation experiments, numerical simulations, and theoretical studies to understand the elastic response of a deforming granular assembly of soft spheres under isotropic loading. Our results for the behavior of the elastic moduli of the system agree very well with experiments. We show that the elasticity partially describes the experimental and numerical results for a system under compressional loads. However, it drastically fails for systems under shear perturbations, particularly for packings without tangential forces and friction. Our work indicates that a correct treatment should include not only the purely elastic response but also collective relaxation mechanisms related to structural disorder and nonaffine motion of grains.

Continuum approach to wide shear zones in quasistatic granular matter

Martin Depken — 2007-02-06T18:25:36-00:00

Physical Review E (Statistical, Nonlinear, and Soft Matter Physics), Vol. 73, No. 3. (2006)

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.

Surface elastic waves in granular media under gravity

L Bonneau — 2006-12-12T17:21:48-00:00

(25 Jan 2006)

Due to the non-linearity of Hertzian contacts, the speed of sound $c$ in granular matter is expected to increase with pressure as $P^1/6$. A static layer of grains under gravity is thus stratified so that bulk waves are refracted toward the surface. We investigate wave propagation in the framework of an elastic description taking into account the main features of granular matter: non-linearity between stress and strain and existence of a yielding transition. We show in this context the existence of waves localised at the free surface --~like Rayleigh waves~-- but with a wave guide effect related to the non-linear Hertz contact. The dispersion relationship shows a discrete number of modes which correspond to modes localized in the sagittal plane but also to transverse modes. The propagation speed of these waves is finally compared to recent measurements performed in the field, at the surface of a sand dune.

Experimental study of sound propagation in a chain of spherical beads

M de Billy — 2006-08-15T20:29:35-00:00

The Journal of the Acoustical Society of America, Vol. 108, No. 4. (2000), pp. 1486-1495.

In this paper are described experimental observations which are concerned by the propagation of pulsed ultrasonic waves transmitted through a limited one dimensional periodic granular medium submitted to a static force. This study—which is limited to a time domain analysis—exhibits experimental results which depend on the polarization of the acoustic excitation. In the case of compressional excitation, spherical Rayleigh type surface waves propagate around the beads. In the case of shear excitation, the experimental recordings point out the existence of a very low signal, the frequency of which is equal to the cut-off frequency of the chain. Moreover it is established that the frequency value varies with the radius of the bead, the normal force applied to the beads, and the mechanical properties of the material. ©2000 Acoustical Society of America.

On the validity of Hertz contact law for granular material

C Coste — 2006-08-15T20:25:27-00:00

European Physical Journal B, Vol. 7, No. 1. (1999), pp. 155-168.