2004/11/11 by J JENKINS, James T. Jenkins, J. Jenkins +3 · 4 citations
Engineering · Materials Science · Physics and Astronomy · #Adhesion, Friction, and Surface Interactions #Granular flow and fluidized beds #Material Dynamics and Properties #cond-mat.soft
paper · pdf · doi:10.1016/j.jmps.2004.06.002
published as Journal of the Mechanics and Physics of Solids 53, 197-225 (2005)
arxiv created 2005/02/27 · arxiv updated 2009/12/01
We consider a random aggregate of identical frictionless elastic spheres that has first been subjected to an isotropic compression and then sheared. We assume that the average strain provides a good description of how stress is built up in the initial isotropic compression. However, when calculating the increment in the displacement between a typical pair of contaction particles due to the shearing, we employ force equilibrium for the particles of the pair, assuming that the average strain provides a good approximation for their interactions with their neighbors. The incorporation of these additional degrees of freedom in the displacement of a typical pair relaxes the system, leading to a decrease in the effective moduli of the aggregate. The introduction of simple models for the statistics of the ordinary and conditional averages contributes an additional decrease in moduli. The resulting value of the shear modulus is in far better agreement with that measured in numerical simulations.