Physics – Condensed Matter – Soft Condensed Matter
Scientific paper
2005-02-27
Journal of the Mechanics and Physics of Solids 53, 197-225 (2005)
Physics
Condensed Matter
Soft Condensed Matter
Scientific paper
10.1016/j.jmps.2004.06.002
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.
Jenkins Jennifer
Johnson Dennis
Makse Hernan
Ragione Luigi La
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