Numerical study of the stress response of two-dimensional dense granular packings

Abstract

We investigate the Green function of two-dimensional dense random packings of grains in order to discriminate between the different theories of stress transmission in granular materials. Our computer simulations allow for a detailed quantitative investigation of the dynamics which is difficult to obtain experimentally. We show that both hyperbolic and parabolic models of stress transmission fail to predict the correct stress distribution in the studied region of the parameters space. We demonstrate that the compressional and shear components of the stress compare very well with the predictions of isotropic elasticity for a wide range of pressures and porosities and for both frictional and frictionless packings. However, the states used in this study do not include the critical isostatic point for frictional particles, so that our results do not preclude the fact that corrections to elasticity may appear at the critical point of jamming, or for other sample preparation protocols, as discussed in the main text. We show that the agreement holds in the bulk of the packings as well as at the boundaries and we validate the linear dependence of the stress profile width with depth.

Critical Scaling in Linear Response of Frictionless Granular Packings near Jamming

“…We numerically study the linear, quasistatic response of systems near the jamming transition. The response of granular media has been widely-studied [11,12,13,14,15,16], but not, we believe, systematically as a function of the distance to the jamming point J. Nor does it seem to have been fully appreciated that the scaling behavior can essentially be captured within linear response.…”

Force Network Ensemble: A New Approach to Static Granular Matter

“…For small enough forces this probes the Green's function of the granular packing and provides crucial information on the effective continuum description of the system. Experiments [77][78][79] and simulations [31,80,81] have shown that the spreading of the load inside the material is not universal but can be along a single broad peak, as is the case for isotropic linear elastic materials, or more anisotropically along two peaks. The response is found to depend on parameters such as friction coefficient, degree of disorder, coordination number and amplitude of applied force.…”

Mechanical properties of inclined frictional granular layers

“…Experimental and numerical works have shown that the linear stress response of granular systems to a point force is well described by (possibly anisotropic) elasticity [36,3,17,24,18,2,15]. In this section, we introduce the framework of orthotropic elasticity, with which numerical response profiles such as those displayed in Fig.…”