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

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 $1000\times 1000$ 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 $\sqrt{Dz}$. $c$ and $D$ are analogous to `propagation' and `diffusion' coefficients. Their values depend on that of the friction coefficient $\mu$. At small $\mu$, we get $c_0-c\propto \mu$ and $D\propto {\mu }^{\beta }$, with $\beta \sim 2.5$, 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.

7 pages, 7 figures, accepted version to Europhys. Lett

References in corpus (4)

• Footprints in Sand: The Response of a Granular Material to Local Perturbations
• Green's function probe of a static granular piling
• Stress response function of a granular layer: quantitative comparison between experiments and isotropic elasticity
• Robust propagation direction of stresses in a minimal granular packing

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• Response of a Hexagonal Granular Packing under a Localized External Force: Exact Results
• Stress response inside perturbed particle assemblies
• Anomalous force diffusion in nearly-ordered packings of frictionless discs