Stress response function of a two-dimensional ordered packing of frictional beads

Abstract

Abstract. -We study the stress profile of an ordered two-dimensional packing of beads in response to the application of a vertical overload localized at its top surface. Disorder is introduced through the Coulombic friction between the grains which gives some indeterminacy and allows the choice of one constrained random number per grain in the calculation of the contact forces. The so-called 'multi-agent' technique we use, lets us deal with systems as large as 1000×1000 grains. We show that the average response profile has a double peaked structure. At large depth z, the position of these peaks grows with cz, while their widths scales like √ Dz. c and D are analogous to 'propagation' and 'diffusion' coefficients. Their values depend on that of the friction coefficient µ. At small µ, we get c0 − c ∝ µ and D ∝ µ β , with β ∼ 2.5, which means that the peaks get closer and wider as the disorder gets larger. This behavior is qualitatively what was predicted in a model where a stochastic relation between the stress components is assumed.

Stress response inside perturbed particle assemblies

“…This crosses over to an anisotropic response function of the double-peak variety further from the source. This double-peak feature is suitably captured by the modified Convection-Wave equation; peak widths scaling linearly with distance, rather than the diffusive form of this equation [9]. These results are consistent with a generalisation from 2D to 3D anisotropic elasticity theories [32].…”

Effects of weak disorder on stress-wave anisotropy in centered square nonlinear granular crystals

“…Previous studies of the static load transfer path in 2D granular systems showed that ordered granular arrays allow the load to be transmitted primarily along lattice vectors [7][8][9][10], while disordered particle arrangements result in complicated force chain networks [7,[10][11][12][13]. The role of force chains in the dynamic load transfer within disordered granular systems has also been studied [14][15][16].…”

“…It has also been suggested that irregularities in particle surface profiles could lead to deviations from Hertzian behavior and reorganization of particles between successive experiments * andreal@caltech.edu † daraio@caltech.edu ‡ amnaya@illinois.edu § geubelle@illinois.edu [23]. Other sources of disorder stem from the redundancy in particle contacts in densely packed arrays and the presence of friction [7,9,10].…”

“…While the majority of load is still transferred along the preferential load path, slight misalignments divert some of the force to neighboring particles [8]. For example, several studies have looked at the effects of weak disorder on the static load transfer path of a triangular or hexagonal array of particles subject to a point load [7][8][9][10]. The presence of disorder causes the ideal sharply peaked response to broaden; the further away one looks from the loading point, the less pronounced the ideal load path since the disorder compounds [7][8][9][10].…”

“…For example, several studies have looked at the effects of weak disorder on the static load transfer path of a triangular or hexagonal array of particles subject to a point load [7][8][9][10]. The presence of disorder causes the ideal sharply peaked response to broaden; the further away one looks from the loading point, the less pronounced the ideal load path since the disorder compounds [7][8][9][10]. Mueggenburg et al experimentally observed the same trends for both quasistatic and dynamic loading conditions for 3D hcp and fcc granular arrays [8].…”