Static response in disk packings

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 Gaussianlike 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.

Reorganization of a dense granular assembly: The unjamming response function

“…We call it the 'unjamming response' function which should be a characteristic feature of the packing configurations and of its reorganization properties. Note that, very recently, similar displacement response experiments have been performed by Moukarzel et al [18].…”

Effects of friction and disorder on the quasistatic response of granular solids to a localized force

“…In the simulations reported in [23] the displacement (rather than the force) response of a 2D packing of disks of three different diameters was measured (in response to a small displacement of a particle at the bottom of the packing). The displacement response is expected to be qualitatively similar to the force response (in isostatic systems the two are equivalent [31,32]).…”

“…In order to obtain insights into this problem it is convenient to consider the simpler geometry of a granular rectangular layer (or slab) resting on a solid support [16], * Electronic address: chayg@pmmh.espci.fr † Electronic address: isaac@eng.tau.ac.il not the least since this class of systems is well researched experimentally [17,18,19,20,21,22,23]. Much like in the case of piles, the cited and other experiments seem to be sending mixed messages concerning the 'correct' description of stress transmission in granular slabs, as some render support to the elliptic descriptions whereas others are compatible with hyperbolic models.…”

Mean-field description of jamming in noncohesive frictionless particulate systems

“…For granular media the problem is particularly acute, as the Green's response has been the subject of substantial debate in recent years (see e.g. [1,2,3] and refs therein). The approximation scheme detailed below circumvents these issues, as we describe below.…”

“…Note that the unphysical singularity at λf /r = 1 is avoided by the stability equation below. It is apparent from (6) that the MMA has reduced the global problem to a local one, in which the response of each contact δf αβ depends only on the interparticle separation r αβ (through which f (r) and f ′ (r) are found), the unit vectorn αβ , and the coordination number for this bead z α , implicit in the summation (3). Before the averaging can be completed, it is necessary to specify how these quantities vary.…”