Typical granular materials are strain-weakening under triaxial compression:  the harder they are pushed the weaker they become, and eventually they fail via characteristic shear banding. A qualitatively different response to compression emerges when individual spherical grains are flexibly linked into linear chains. We show that random packings of granular chains behave similar to polymers in that entanglement can lead to to strain-stiffening. For short chain lengths, the chain packings yield when the shear stress exceeds a the scale of the confining pressure, similar to packings of individual spherical particles. However, packings of chains which are long enough to form loops exhibit strain-stiffening, in which the effective stiffness of the material increases with strain. The latter packings can sustain stresses orders of magnitude greater than the confining pressure, and do not yield until the chain links break. X-ray tomography reveals that the strain-stiffening packings contain system-spanning clusters of entangled chains. Since entanglement implies a multitude of loops these packings also exhibit a large void space. This opens up new possibilities for very lightweight yet exceptionally strong random packings.

1. •Eric Brown, Alice Nasto, Athanasios G. Athanassiadis, and Heinrich M. Jaeger, “Strain-stiffening in random packings of entangled granular chains”, Phys. Rev. Lett. 108, 108302 (2012). pdf file
   

The data above give the compressive stress \tau as a function of compressive strain \gamma for chain packings. For each of these packings chains of a given length, measured in terms of the number N of beads that are flexibly connected, are randomly packed into a cylinder with flexible (rubber) walls and then compressed in an Instron tester. Single spheres have N = 1.  Note how the stress increases significantly once N>8; in this type of granular polymer N=8 corresponds to the persistence length, i.e., the number of beads in the tightest chain loop. 

X-ray tomography indicates that the change in behavior is related to the ability of chains to form entangled clusters that span the sample: the images on the right show clusters of all entangled chains for N=5 and N=10, highlighting the dramatic increase in the overall extent of entangled chains as N crosses the strain stiffening threshold.  These images are not from simulations but individual beads as well as their neighbors in every chain were identified and rendered from x-ray tomography data, such as shown below.