||Emergent Strain-Stiffening in Interlocked Granular Chains
Dumont, Denis ,
Houze, Maurine ,
Rambach, Paul ,
Salez, Thomas ,
Patinet, SylvainDamman, Pascal
p.1707 , 2017-12-15 , Cornell University Library
Granular chain packings exhibit a striking emergent strain-sti ening 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-ampli cation 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. Speci cally, the resistance force is found to vary according to the universal relation: log F ～ μ√NΦ11/8 z/b, where μ is the friction coe cient between two elementary beads, b is their size, and is the volume fraction of chain beads when semi-diluted in a surrounding medium of unconnected beads. Our study suggests that theories normally con ned 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.