A Scalar Arching Model

We propose an alternative approach to count the microscopic static configurations of granular packs under gravity by considering arches. This strategy simplifies the problem of filtering out configurations that are not mechanically stable, opening the way for a range of granular models to be studied via ensemble theory. Following this arch-based approach, we have obtained the exact density of states for a two-dimensional non-interacting rigid arch model of granular assemblies...

We present a numerical model for a two dimensional (2D) granular assembly, falling in a rectangular container when the bottom is removed. We observe the occurrence of cracks splitting the initial pile into pieces, like in experiments. We study in detail various mechanisms connected to the `discontinuous decompaction' of this granular material. In particular, we focus on the history of one single long range crack, from its origin at one side wall, until it breaks the assembly ...

In this paper, we describe how we can precisely produce complex and various dynamic morphological features such as structured and chaotic features which occur in sand pilings (piles, avalanches, internal collapses, arches) , in flowing fluids (laminar flowing, Kelvin-Helmholtz and Von Karmann eddies), and in cohesive pastes (twist-and-turn oozing and packing) using only a single unified model, called "mesoscopic model". This model is a physically-based particle model whose be...

The two most commonly used methods to model the behaviour of granular flows are discrete element and continuum mechanics simulations. These approaches concentrate on the deterministic description of particle or bulk material motion. Unlike these approaches, this paper introduces an alternative model that describes the stochastic dynamics of the void spaces under the action of gravity. The model includes several key phenomena which are observed in deforming granular media, suc...

We present a stochastic model of dynamically interacting grains in one dimension, in the presence of a low vibrational intensity, to investigate the effect of shape on the statics and dynamics of the compaction process. Regularity and irregularity in grain shapes are shown to be centrally important in determining the statics of close-packing states, as well as the nature of zero- and low-temperature dynamics in this columnar model.

We describe a new continuum approach to the modelling of stress propagation in static granular media, focussing on the conical sandpile created from a point source. We argue that the stress continuity equations should be closed by means of scale-free, local constitutive relations between different components of the stress tensor, encoding the construction history of the pile: this history determines the organization of the grains, and thereby the local relationship between st...

An arch will grow on a rapidly deployed thin string in contact with a rigid plane. We present a qualitative model for the growing structure involving the amplification, rectification, and advection of slack in the presence of a steady stress field, validate our assumptions with numerical experiments, and pose new questions about the spatially developing motions of thin objects.

The question when and how dense granular materials start to flow under stress, despite many industrial and geophysical applications, remains largely unresolved. We develop and test a simple equation for the onset of quasi-static flows of granular materials which is based on the frictional aging of the granular packing. The result is a non-monotonic stress-strain relation which - akin to classical friction - is independent of the shear rate. This relation suffices to understan...

We investigate the morphology and mechanics of a naturally curved elastic arch loaded at its center and frictionally supported at both ends on a flat, rigid substrate. Through systematic numerical simulations, we classify the observed behaviors of the arch into three distinct types of configurations in terms of the arch geometry and the coefficient of static friction with the substrate. A linear theory is developed based on a planar elastica model combined with Amontons-Coulo...

We proposed a toy model of granular compaction which includes some resistance due to granular arches. In this model, the solid/solid friction of contacting grains is a key parameter and a slipping threshold Wc is defined. Realistic compaction behaviors have been obtained. Two regimes separated by a critical point Wc* of the slipping threshold have been emphasized : (i) a slow compaction with lots of paralyzed regions, and (ii) an inverse logarithmic dynamics with a power law ...