  Granular chain packings exhibit a striking emergent strain-stiffening
behavior despite the individual looseness of the constitutive chains. Using
indentation experiments on such assemblies, we measure an exponential increase
in the collective resistance force $F$ with the indentation depth $z$, and with
the square root of the number $\mathcal{N}$ of beads per chain. These two
observations are respectively reminiscent of the self-amplification of friction
in a capstan or in interleaved books, as well as the physics of polymers. The
experimental data are well captured by a novel model based on these two
ingredients. Specifically, the resistance force is found to vary according to
the universal relation: $\log F \sim \mu \sqrt{\mathcal{N}} \Phi^{11/8}z/ b $,
where $\mu$ is the friction coefficient between two elementary beads, $b$ is
their size, and $\Phi$ is the volume fraction of chain beads when semi-diluted
in a surrounding medium of unconnected beads. Our study suggests that theories
normally confined to the realm of polymer physics at a molecular level can be
used to explain phenomena at a macroscopic level. This class of systems enables
the study of friction in complex assemblies, with practical implications for
the design of new materials, the textile industry, and biology.
