Stress Transmission and Isostatic States of Non-Rigid Particulate Systems

Blumenfeld, Raphaël

doi:10.1007/0-387-32153-5_10

Cited by 5 publications

(4 citation statements)

References 23 publications

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“…Here, we consider the special case M = 0, in line with the force chain buckling model in [20]. Equation (6) can be used to determine the couple stress μ 2 , once σ 21 is established from (4)- (5). In cases of constant coefficients G and T , and hence constant GT , the characteristics comprise two families of straight parallel lines, w 1 and w 2 , with slopes ±λ = ± √ GT .…”

Section: Analytical Solutions For Cauchy Stresses With Straight Charamentioning

confidence: 99%

“…For the constant closure coefficients considered in (4)-(6), the solution scheme proceeds in three steps: first, equations (4) and (5) are solved for σ 11 and σ 21 ; second, σ 22 and σ 12 are determined from the first two closure relations; and third μ 2 is obtained from (6). Couple stress μ 1 is obtained from the third closure equation (3), but here we focus on the case M = 0.…”

Section: Numerical Solutionsmentioning

confidence: 99%

“…The question that then arises is under what states might the condition of statically determinate stresses or isostaticity be reasonably assumed in a continuum as well as at the particle scale? Before proceeding, note that the issue of compliance for frictionless (Hertzian) contact was addressed by Blumenfeld [6]; therein he showed that provided the mean coordination number in d-dimensions is d + 1, a macroscopic system of compliant but frictionless particles can be mapped onto an equivalent assembly of perfectly rigid particles that approximately supports the same stress field. The error or discrepancy between the two stress fields decays with system size according to a power law.…”

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Isostaticity in Cosserat continuum

2012

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Under conditions of isostaticity in granular media, the contact forces for all particles are statically determinate and forces can be computed without recourse to deformation equations or constitutive relationships. Given that stresses represent spatial averages of inter-particle forces, the stressequilibrium equations for the isostatic state form a hyperbolic system of partial differential equations that describe the internal stress state using only boundary tractions. In this paper, we consider a Cosserat medium and propose closure relationships in terms of stresses and couple stresses from observations of stress variations in the critical state regime from discrete element simulations and experiments on sand, even though the isostatic condition is only satisfied in an average sense. It is shown that the governing equations are hyperbolic, which can be solved using the method of characteristics. Examples of both analytic and numerical solutions are presented. These examples clearly demonstrate that stress chains (characteristic lines) form oblique angles with the assumed direction of the force chains.

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Section: Analytical Solutions For Cauchy Stresses With Straight Charamentioning

confidence: 99%

Section: Numerical Solutionsmentioning

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Isostaticity in Cosserat continuum

2012

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“…Why these idealized systems are useful to understanding general granular materials has been discussed in 20 . 21 Stresses in planar systems are governed by…”

Section: The Entropic Formalism and Mechanical Stressesmentioning

confidence: 99%

On entropic characterization of granular materials

Blumenfeld

2007

World Scientific Lecture Notes in Complex Systems

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This chapter presents recent developments in entropic characterization of granular materials. The advantages of the formalism and its use are illustrated for calculation of structural characteristics, such as porosity fluctuations and the throat size distribution. I discuss the relations between the entropic formalism and stress transmission. It is argued that a new sub-ensemble of loading distributions is necessary, which introduces a tensor temperature-like quantity named angoricity.

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Stress transmission and incipient yield flow in dense granular materials

Blumenfeld¹

2010

AIP Conference Proceedings

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Abstract. Jammed granular matter transmits stresses non-uniformly like no conventional solid, especially when it is on the verge of failure. Jamming is caused by self-organization of granular matter under external loads, often giving rise to networks of force chains that support the loads non-uniformly. An ongoing debate in the literature concerns the correct way to model the static stress field in such media: good old elasticity theory or newcomer isostaticity theory. The two differ significantly and, in particular in 2D, isostaticity theory leads naturally to force chain solutions. More recently, it has been proposed that real granular materials are made of mixtures of regions, some behaving elastically and some isostatically. The theory to describe these systems has been named stato-elasticity.In this paper, I first present the rationale for stato-elasticity theory. An important step towards the construction of this theory is a good understanding of stress transmission in the regions of pure isostatic states. A brief description is given of recently derived general solutions for 2D isostatic regions with nonuniform structures, which go well beyond the over-simplistic picture of force chains.I then show how the static stress equations are related directly to incipient yield flow and derive the equations that govern yield and creep rheology of dense granular matter at the initial stages of failure. These equations are general and describe strains in granular materials of both rigid and compliant particles.

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Stress Transmission and Isostatic States of Non-Rigid Particulate Systems

Cited by 5 publications

References 23 publications

Isostaticity in Cosserat continuum

Isostaticity in Cosserat continuum

On entropic characterization of granular materials

Stress transmission and incipient yield flow in dense granular materials

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