American Institute of Mathematical Sciences

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November  2003, 3(4): 601-618. doi: 10.3934/dcdsb.2003.3.601

Discrete models of force chain networks

Joshua E.S. Socolar 1,

1. 

Physics Department, Duke University, Durham, NC 27708, United States

Received  December 2002 Revised  May 2003 Published  August 2003

A fundamental property of any material is its response to a localized stress applied at a boundary. For granular materials consisting of hard, cohesionless particles, not even the general form of the stress response is known. Directed force chain networks (DFCNs) provide a theoretical framework for addressing this issue, and analysis of simplified DFCN models reveal both rich mathematical structure and surprising properties. We review some basic elements of DFCN models and present a class of homogeneous solutions for cases in which force chains are restricted to lie on a discrete set of directions.
Keywords: elasticity theory., Granular materials.
Mathematics Subject Classification: 74E20,74B20, 70C20, 34B1.
Citation: Joshua E.S. Socolar. Discrete models of force chain networks. Discrete & Continuous Dynamical Systems - B, 2003, 3 (4) : 601-618. doi: 10.3934/dcdsb.2003.3.601
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