arXiv subjects

P. Claudin

Publications and source records attributed to P. Claudin.

47 records · Page 3Linked to original sources

arXiv2000

Force chain splitting in granular materials: a mechanism for large scale pseudo-elastic behaviour

We investigate both numerically and analytically the effect of strong disorder on the large scale properties of the hyperbolic equations for stresses proposed in \protect\cite{bcc,wcc}. The physical mechanism that we model is the local splitting of the force chains (the characteristics of the hyperbolic equation) by packing defects. In analogy with the theory of light diffusion in a turbid medium, we propose a Boltzmann-like equation to describe these processes. We show that, for isotropic packings, the resulting large scale effective equations for the stresses have exactly the same structure as those of an elastic body, despite the fact that no displacement field needs to be introduced at all. Correspondingly, the response function evolves from a two peak structure at short scales to a broad hump at large scales. We find, however, that the Poisson ratio is anomalously large and incompatible with classical elasticity theory that requires the reference state to be thermodynamically stable.

cond-mat↗

arXiv1999

Jamming and Stress Propagation in Granular Materials

We have recently developed some simple continuum models of static granular media which display "fragile" behaviour: they predict that the medium is unable to support certain types of infinitesimal load (which we call "incompatible" loads) without plastic rearrangement. We argue that a fragile description may be appropriate when the mechanical integrity of the medium arises adaptively, in response to a load, through an internal jamming process. We hypothesize that a network of force chains (or "granular skeleton") evolves until it can just support the applied load, at which point it comes to rest; it then remains intact so long as no incompatible load is applied. Our fragile models exhibits unusual mechanical responses involving hyperbolic equations for stress propagation along fixed characteristics through the material. These characteristics represent force chains; their arrangement expressly depends on the construction history. Thus, for example, we predict a large difference in the stress pattern beneath two conical piles of sand, one poured from a point source and one created by sieving.

cond-mat.mtrl-sci↗

arXiv1998

Jamming and Stress Propagation in Particulate Matter

We present simple models of particulate materials whose mechanical integrity arises from a jamming process. We argue that such media are generically "fragile", that is, they are unable to support certain types of incremental loading without plastic rearrangement. In such models, fragility is naturally linked to the marginal stability of force chain networks (granular skeletons) within the material. Fragile matter exhibits novel mechanical responses that may be relevant to both jammed colloids and cohesionless assemblies of poured, rigid grains.

cond-mat.stat-mech↗

arXiv1998

Development of Stresses in Cohesionless Poured Sand

The pressure distribution beneath a conical sandpile, created by pouring sand from a point source onto a rough rigid support, shows a pronounced minimum below the apex (`the dip'). Recent work of the authors has attempted to explain this phenomenon by invoking local rules for stress propagation that depend on the local geometry, and hence on the construction history, of the medium. We discuss the fundamental difference between such approaches, which lead to hyperbolic differential equations, and elastoplastic models, for which the equations are elliptic within any elastic zones present .... This displacement field appears to be either ill-defined, or defined relative to a reference state whose physical existence is in doubt. Insofar as their predictions depend on physical factors unknown and outside experimental control, such elastoplastic models predict that the observations should be intrinsically irreproducible .... Our hyperbolic models are based instead on a physical picture of the material, in which (a) the load is supported by a skeletal network of force chains ("stress paths") whose geometry depends on construction history; (b) this network is `fragile' or marginally stable, in a sense that we define. .... We point out that our hyperbolic models can nonetheless be reconciled with elastoplastic ideas by taking the limit of an extremely anisotropic yield condition.

cond-mat.stat-mech↗

arXiv1998

Jamming, Force Chains and Fragile Matter

We consider materials whose mechanical integrity is the result of a jamming process. We argue that such media are generically "fragile": unable to support certain types of incremental loading without plastic rearrangement. Fragility is linked to the marginal stability of force chain networks within the material. Such ideas may be relevant to jammed colloids and poured sand. The crossover from fragile (when particles are rigid) to elastoplastic behavior is explored.

cond-mat↗

arXiv1997

A Scalar Arching Model

In this paper we propose an extension of the model of Liu, Coppersmith et al., in order to allow for arch formation. This extended model qualitatively captures interesting properties of granular materials due to fluctuations of stress paths, such as stress fluctuations and stick-slip motion.

cond-mat↗

arXiv1997

Models of stress propagation in granular media

Stress patterns in static granular media exhibit unusual features when compared to either liquids or elastic solids. Qualitatively, we attribute these features to the presence of `stress paths', whose geometry depends on the construction history and controls the propagation of stresses. Stress paths can cause random focussing of stresses (large fluctuations) as well as systematic deflections (arching). We describe simple physical models that capture some of these effects. In these models, the `stress paths' become identified with the characteristic `light rays' of wavelike (hyperbolic) equations for force propagation. Such models account for the `pressure dip' below conical sandpiles built by pouring from a point source, and explain qualitatively the large stress fluctuations observed experimentally in granular matter. The differences between this approach and more conventional modelling strategies (based on elastoplastic or rigid-plastic models) are highlighted, focusing on the role of boundary conditions. Our models provide a continuum picture in which granular materials are viewed as fragile matter, able to support without rearranging only a subset of the static external loadings admissible for a normal elastic solid.

cond-mat↗

arXiv1997

Models of stress fluctuations in granular media

We investigate in detail two models describing how stresses propagate and fluctuate in granular media. The first one is a scalar model where only the vertical component of the stress tensor is considered. In the continuum limit, this model is equivalent to a diffusion equation (where the rôle of time is played by the vertical coordinate) plus a randomly varying convection term. We calculate the response and correlation function of this model, and discuss several properties, in particular related to the stress distribution function. We then turn to the tensorial model, where the basic starting point is a wave equation which, in the absence of disorder, leads to a ray-like propagation of stress. In the presence of disorder, the rays acquire a diffusive width and the angle of propagation is shifted. A striking feature is that the response function becomes negative, which suggests that the contact network is mechanically unstable to very weak perturbations. The stress correlation function reveals characteristic features related to the ray-like propagation, which are absent in the scalar description. Our analytical calculations are confirmed and extended by a numerical analysis of the stochastic wave equation.

cond-mat↗

arXiv1996

Stress Propagation and Arching in Static Sandpiles

We present a new approach to the modelling of stress propagation in static granular media, focussing on the conical sandpile constructed from a point source. We view the medium as consisting of cohesionless hard particles held up by static frictional forces; these are subject to microscopic indeterminacy which corresponds macroscopically to the fact that the equations of stress continuity are incomplete -- no strain variable can be defined. We propose that in general the continuity equations should be closed by means of a constitutive relation (or relations) between different components of the (mesoscopically averaged) stress tensor. The primary constitutive relation relates radial and vertical shear and normal stresses (in two dimensions, this is all one needs). We argue that the constitutive relation(s) should be local, and should encode the construction history of the pile: this history determines the organization of the grains at a mesoscopic scale, and thereby the local relationship between stresses. To the accuracy of published experiments, the pattern of stresses beneath a pile shows a scaling between piles of different heights (RSF scaling) which severely limits the form the constitutive relation can take ...

cond-mat↗

arXiv1996

Static avalanches and Giant stress fluctuations in Silos

We propose a simple model for arch formation in silos. We show that small pertubations (such as the thermal expansion of the beads) may lead to giant stress fluctuations on the bottom plate of the silo. The relative amplitude $Δ$ of these fluctuations are found to be power-law distributed, as $Δ^{-τ}$, $τ\simeq 1.0$. These fluctuations are related to large scale `static avalanches', which correspond to long-range redistributions of stress paths within the silo.

cond-mat↗

arXiv1995

Glassy Solutions of the Kardar-Pasrisi-Zhang Equation

It is shown that the mode-coupling equations for the strong-coupling limit of the KPZ equation have a solution for d>4 such that the dynamic exponent z is 2 (with possible logarithmic corrections) and that there is a delta function term in the height correlation function = (A/k^{d+4-z}) δ(w/k^z) where the amplitude A vanishes as d -> 4. The delta function term implies that some features of the growing surface h(x,t) will persist to all times, as in a glassy state.

cond-mat↗