||Emergent Strain-Stiffening in Interlocked Granular Chains
Dumont, Denis ,
Houze, Maurine ,
Rambach, Paul ,
Salez, Thomas ,
Patinet, SylvainDamman, Pascal
p.1707 , 2017-06-26 , Cornell University Library
Granular-chain packings exhibit a striking emerging strain-stiffening behavior despite the individual looseness of their constitutive chains. Using indentation experiments on such assemblies, we measure an exponential increase of 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 assemblies of sheets, as well as the physics of polymers. The experimental data is 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√NΦ5/8 z/b, where μ is the friction coefficient between two elementary beads, b is the size of such a bead, and Φ is the volume fraction of chains when semi-diluted in a surrounding medium of unconnected beads. Beyond the intrinsic similarity with the polymeric glass transition, this system allows to study friction in complex assemblies, with practical implications for the design of new materials, textile industry, and biology.