Wouter G Ellenbroek | PubMed Health

PubMed2006

Sheared force networks: anisotropies, yielding, and geometry.

A scenario for the yielding of granular matter is presented by considering the ensemble of force networks for a given contact network and applied shear stress tau. As tau is increased, the probability distribution of contact forces becomes highly anisotropic, the difference between average contact forces along minor and major axes grows, and the allowed networks span a shrinking subspace of all force networks. Eventually, contacts start to break, and at the maximal shear stress the packing becomes effectively isostatic. The size of the allowed subspace exhibits simple scaling properties, which lead to a prediction for the yield stress for packings of an arbitrary contact number.

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PubMed2004

Ensemble theory for force networks in hyperstatic granular matter.

An ensemble approach for force networks in static granular packings is developed. The framework is based on the separation of packing and force scales, together with an a priori flat measure in the force phase space under the constraints that the contact forces are repulsive and balance on every particle. In this paper we will give a general formulation of this force network ensemble, and derive the general expression for the force distribution P(f). For small regular packings these probability densities are obtained in closed form, while for larger packings we present a systematic numerical analysis. Since technically the problem can be written as a noninvertible matrix problem (where the matrix is determined by the contact geometry), we study what happens if we perturb the packing matrix or replace it by a random matrix. The resulting P(f) 's differ significantly from those of normal packings, which touches upon the deep question of how network statistics is related to the underlying network structure. Overall, the ensemble formulation opens up a different perspective on force networks that is analytically accessible, and which may find applications beyond granular matter.

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