On the Granular Stress-Geometry Equation
Eric DeGiuli, Christian Schoof
TL;DR
This paper derives a key stress-geometry equation for 2D granular materials using discrete calculus, revealing how voids, stress transmission, and packing fabric influence material behavior.
Contribution
It introduces a novel stress-geometry equation for rigid granular materials, linking voids, stress transmission, and fabric in a mean-field framework.
Findings
Voids cannot carry stress
Stress transmission is elliptic and related to anisotropic elasticity
Packing fabric significantly influences stress distribution
Abstract
Using discrete calculus, we derive the missing stress-geometry equation for rigid granular materials in two dimensions, in the mean-field approximation. We show that (i) the equation imposes that the voids cannot carry stress, (ii) stress transmission is generically elliptic and has a quantitative relation to anisotropic elasticity, and (iii) the packing fabric plays an essential role.
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