### Tuesday, 12 October 2004 - 10:55 AM

### This presentation is part of : Torquato Symposium

### Effective Moduli of a Random Aggregate of Identical, Frictionless Spheres

**James Thomas Jenkins**, Department of Theoretical and Applied Mechanics- Cornell University, 221 Kimball Hall, Ithaca, NY 14853 and Luigi La Ragione, Dipartimento di Ingegneria Civile e Ambientale- Politecnico di Bari, Via Re David 200, Bari, 70125, Italy.
In a recent paper, Jenkins, Johnson, La Ragione & Makse (J. Mech. Phys. Solids, 2004) propose a method to calculate the effective elastic moduli for a random aggregate of identical frictionless spheres. They introduce fluctuations in the displacements of typical pair of particles and they determine these deviations from the average motion using the equilibrium equations. The solution of the force balance yields an expression for the fluctuations that involves the packing geometry of the aggregate. The packing geometry is characterized by tensors which, together with the coordination number (the average number of contacts per particle) and the porosity, may be interpreted as state variables for the aggregate. Here, we show how simple statistical characterizations of these tensors provide an analytical expression for the fluctuations. The terms that are modelled are conditional averages of the local state variables and products of these variables.

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