Jamming and Stress Propagation in Granular Materials

TL;DR

This paper introduces continuum models for granular materials that exhibit fragile behavior, where the internal force network adapts through jamming to support loads, leading to unique stress propagation patterns dependent on history.

Contribution

It proposes a new fragile modeling framework for granular media that captures history-dependent force chain evolution and hyperbolic stress propagation.

Findings

Force chains evolve until load support is just achieved

Stress propagates along fixed characteristics related to force chains

Different pile formation methods result in distinct stress patterns

Abstract

We have recently developed some simple continuum models of static granular media which display "fragile" behaviour: they predict that the medium is unable to support certain types of infinitesimal load (which we call "incompatible" loads) without plastic rearrangement. We argue that a fragile description may be appropriate when the mechanical integrity of the medium arises adaptively, in response to a load, through an internal jamming process. We hypothesize that a network of force chains (or "granular skeleton") evolves until it can just support the applied load, at which point it comes to rest; it then remains intact so long as no incompatible load is applied. Our fragile models exhibits unusual mechanical responses involving hyperbolic equations for stress propagation along fixed characteristics through the material. These characteristics represent force chains; their arrangement expressly depends on the construction history. Thus, for example, we predict a large difference in the stress pattern beneath two conical piles of sand, one poured from a point source and one created by sieving.