Emergent Strain Stiffening in Interlocked Granular Chains

Abstract : 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 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 ∼ μ √N Φ^11/8 z/b, where μ is the friction coefficient between two elementary beads, b is their size, and Φ is the volume fraction of chain beads when semidiluted 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.
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Physical Review Letters, American Physical Society, 2018, 120 (8), pp.088001. 〈10.1103/PhysRevLett.120.088001〉
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Denis Dumont, Maurine Houze, Paul Rambach, Thomas Salez, Sylvain Patinet, et al.. Emergent Strain Stiffening in Interlocked Granular Chains. Physical Review Letters, American Physical Society, 2018, 120 (8), pp.088001. 〈10.1103/PhysRevLett.120.088001〉. 〈hal-01803414〉

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