Green’s function measurements of force transmission in 2D granular materials

Abstract

We describe experiments that probe the response to a point force of 2D granular systems under a variety of conditions. Using photoelastic particles to determine forces at the grain scale, we obtain ensembles of responses for the following particle types, packing geometries and conditions: monodisperse ordered hexagonal packings of disks, bidisperse packings of disks with different amount of disorder, disks packed in a regular rectangular lattice with different frictional properties, packings of pentagonal particles, systems with forces applied at an arbitrary angle at the surface, and systems prepared with shear deformation, hence with texture or anisotropy. We experimentally show that disorder, packing structure, friction and texture significantly affect the average force response in granular systems. For packings with weak disorder, the mean forces propagate primarily along lattice directions. The width of the response along these preferred directions grows with depth, increasingly so as the disorder of the system grows. Also, as the disorder increases, the two propagation directions of the mean force merge into a single direction. The response function for the mean force in the most strongly disordered system is quantitatively consistent with an elastic description for forces applied nearly normally to a surface, but this description is not as good for non-normal applied forces. These observations are consistent with recent predictions of Bouchaud et al. [Bouchaud et al., Euro. Phys. J. E4 451 (2001); Socolar et al., Euro. Phys. J. E7 353 (2002)] and with the anisotropic elasticity models of Goldenberg and Goldhirsch [Goldenberg & Goldhirsch, Phys. Rev. Lett. 89 084302 (2002)]. At this time, it is not possible to distinguish between these two models. The data do not support a diffusive picture, as in the q-model, and they are in conflict with data by Rajchenbach [Da Silva & Rajchenbach, Nature 406 708 (2000)] that indicate a parabolic response for a system consisting of cuboidal blocks. We also explore the spatial properties of force chains in an anisotropic textured system created by a nearly uniform shear. This system is characterized by stress chains that are strongly oriented along an angle of 45 o , corresponding to the compressive direction of the shear deformation. In this case, the spatial correlation function for force has a range of only one particle size in the direction transverse to the chains, and varies as a power law in the direction Preprint submitted to Elsevier Science of the chains, with an exponent of -0.81. The response to forces is strongest along the direction of the force chains, as expected. Forces applied in other directions are effectively refocused towards the strong force chain direction.

Force chain and contact cycle evolution in a dense granular material under shallow penetration

“…The long m-force chains, m ≥ 6, increasingly concentrate directly below the punch, fanning downward and outward from the punch face, as indentation proceeds. The spatial distribution of these chains is similar in shape to that observed in the experiments of Geng et al (2003), in particular, the mean field response (i.e. averaged over many realisations) to a concentrated force at the boundary of an assembly of bidisperse photoelastic disks.…”

“…Among the most studied is the formation of self-organised load-bearing particle groups called "force chains" which vary in size from a few to many grains that can percolate through the whole sample (e.g. Geng et al, 2003;Oda and Kazama, 1998;Oda et al, 2004;Tordesillas, 2007). From the standpoint of material characterisation and modelling, these emergent structures pose great scientific challenges as their analytical formulation embodies strong nonlinearities and multiscale dynamics in space and time.…”

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.…”

Strain tensor determination of compressed individual silica sand particles using high-energy synchrotron diffraction

“…Photoelastic materials were also used to visualize stress distribution and force chains in granular materials [13][14][15][16]; however, it is very difficult to extract force values from these images.…”