Elementary volumes distribution in 2D granular solids


Statistical mechanics of granular solids have been explored in recent decades either with elementary volume ensembles [1] or with contact force ensembles [2]. This work is based on the former approach dealing with the volume distribution of “quadron” [3], which has a strong advantage in discussing the inter-dependence between the above two approaches [4]. We systematically prepared several 2D granular packs, varying interparticle friction, initial generation states and disc size distribution. Then we studied their effect on quadron volume distribution, mean coordination number, and packing fraction [5]. Our findings are summarized as follows. The quadron volume distribution can be well described by a unique gamma distribution by normalizing it with its mean. This mean quadron volume can be roughly evaluated by the mean coordination number or interparticle friction under our packing protocol. Moreover, the rattlers (non-force carrying particles) volume fraction and rattler-free packing fraction are primarily controlled by the mean coordination number, but the former is affected by the initial state, while the latter by the disc size distribution.

[1] T. Mogami, Soils and Foundations 5(2), 26, 1965; S. Edwards and R. Oakeshott, Physica D 38, 88, 1989; T. Aste, T. Di Matteo, M. Saadatfar, T. Senden, M. Schroter, and H. Swinney, EPL 79, 24003, 2007; C. Song, P. Wang, and H. Makse, Nature 453, 629, 2008.
[2] L. Rothenburg, Ph.D dissertation, Carleton University, 1980; K. Bagi, Powders and grains, 1997; J.D. Goddard, Int. J. Solids and Struct., 2004; B.P. Tighe, A.R.T. van Eerd, T.J.H. Vlugt, PRL, 100, 238001, 2008.
[3] R. C. Ball and R. Blumenfeld, Phys. Rev. Lett. 88, 115505, 2002; R. Blumenfeld and S. Edwards, Phys. Rev. Lett. 90, 114303, 2003.
[4] R. Blumenfeld, J.F. Jordan, S.F. Edwards, PRL, 109, 238001, 2012.
[5] T. Matsushima, R. Blumenfeld, Powders and Grains 2013.

Designed by CSS.Design Sample