Emergent Strain-Stiffening in Interlocked Granular Chains

In nature and architecture, a wide variety of stable structures are formed from dense assemblies of randomly-distributed objects, as illustrated by the various shapes of bird nests. Most physical studies focus on highly anisotropic objects that ensure a solid-like collective behavior and thus the great stability of their assembly. In this presentation, we investigate the effective mechanical rigidity of granular-chain assemblies from indentation experiments. Our observations show an exponential growth of the resistance force with the product of two factors: the indentation depth and the square root of the number of beads per chain. The first factor is reminiscent of the self-amplification of friction in a capstan, as well as in interleaved assemblies of sheets, where the increase in resistance is created by, and proportional to, the force exerted by the operator. The second factor points towards the central role played by topological constraints, in a way that is similar to polymer physics. We propose a novel interlocking model based on those two ingredients, and confront it to the experimental data.