Measurement of Indeterminacy in Packings of Perfectly Rigid Disks

Abstract

Static packings of perfectly rigid particles are investigated theoretically and numerically. The problem of finding the contact forces in such packings is formulated mathematically. Letting the values of the contact forces define a vector in a high-dimensional space enable us to show that the set of all possible contact forces is convex, facilitating its numerical exploration. It is also found that the boundary of the set is connected with the presence of sliding contacts, suggesting that a stable packing should not have more than 2M-3N sliding contacts in two dimensions, where M is the number of contacts and N is the number of particles. These results were used to analyze packings generated in different ways by either molecular dynamics or contact dynamics simulations. The dimension of the set of possible forces and the number of sliding contacts agrees with the theoretical expectations. The indeterminacy of each component of the contact forces are found, as well as the an estimate for the diameter of the set of possible contact forces. We also show that contacts with high indeterminacy are located on force chains. The question of whether the simulation methods can represent a packing's memory of its formation is addressed.

arXiv comment12 pages, 13 figures, submitted to Phys Rev E

References in corpus (3)

• Force network ensemble: a new approach to static granular matter
• Geometric origin of mechanical properties of granular materials
• Global Equation of State of two-dimensional hard sphere systems

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• Quasi-rigidity: some uniqueness issues
• Extent of force indeterminacy in packings of frictional rigid disks
• Origin of Corrections to Mean-field at the Onset of Unjamming
• Bounds on the shear load of cohesionless granular matter
• Resolving Force Indeterminacy in Contact Dynamics Using Compatibility Conditions
• Statistical Inference for Disordered Sphere Packings