Static response in disk packings

TL;DR

This study investigates how forces propagate in granular disk packings, revealing Gaussian-like diffusive behavior experimentally and wave-like responses in frictionless simulations, highlighting differences between real and modeled systems.

Contribution

The paper provides experimental and numerical analysis of displacement responses in granular packings, comparing diffusive and wave-like stress propagation behaviors.

Findings

Experimental response broadens as square root of distance, consistent with diffusive theories.

Numerical simulations show double-peaked, wave-like stress responses.

Discrepancies between experimental and simulation results are discussed.

Abstract

We present experimental and numerical results for displacement response functions in packings of rigid frictional disks under gravity. The central disk on the bottom layer is shifted upwards by a small amount, and the motions of disks above it define the displacement response. Disk motions are measured with the help of a still digital camera. The responses so measured provide information on the force-force response, that is, the excess force at the bottom produced by a small overload in the bulk. We find that, in experiments, the vertical-force response shows a Gaussian-like shape, broadening roughly as the square root of distance, as predicted by diffusive theories for stress propagation in granulates. However, the diffusion coefficient obtained from a fit of the response width is ten times larger than predicted by such theories. Moreover we notice that our data is compatible with a crossover to linear broadening at large scales. In numerical simulations on similar systems (but without friction), on the other hand, a double-peaked response is found, indicating wave-like propagation of stresses. We discuss the main reasons for the different behaviors of experimental and model systems, and compare our findings with previous works.