Physics – Condensed Matter
Scientific paper
2000-11-13
Physics
Condensed Matter
7 pages, 6 figures, An incorrect definition of the Poisson ratio in dimensions not equal to 3 was amended. The conclusions are
Scientific paper
10.1007/s101890170100
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.
Bouchaud Jean-Philippe
Claudin Philippe
Levine Dov
Otto Matthias
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