Stress transmission and isostatic states of non-rigid particulate systems

Details Stress transmission and isostatic states of non-rigid particulate systems Stress transmission and isostatic states of non-rigid particulate systems

2005-01-28

arxiv.org/abs/cond-mat/0501700v1

Physics

Condensed Matter

Soft Condensed Matter

6 pages, 3 figures included, to appear in "IMA Volume in Mathematics and its Applications"

Scientific paper

The isostaticity theory for stress transmission in macroscopic planar particulate assemblies is extended here to non-rigid particles. It is shown that, provided that the mean coordination number in $d$ dimensions is $d+1$, macroscopic systems can be mapped onto equivalent assemblies of perectly rigid particles that support the same stress field. The error in the stress field that the compliance introduces for finite systems is shown to decay with size as a power law. This leads to the conclusion that the isostatic state is not limited to infinitely rigid particles both in two and in three dimensions, and paves the way to an application of isostaticity theory to more general systems.

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