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Geometry, elasticity, and transport in fiber networks

MSC : Marc Durand, Gérald Gurtner

Various elastic systems can be understood as networks of interconnected rods which deform by a combination of bending, stretching, twisting and shearing mechanisms. Examples include polymer gels, protein networks and cytoskeletal structures, crystal atomic lattices and granular materials, paper, wood, foams, and bones. Due to its slender geometry, the mechanical and transport properties of a fiber are easy to calculate. Nonetheless, the mechanical and transport properties of an assembly of such fibers are much more difficult to predict. We are conducting analytical and numerical studies on the mechanical an electric properties of fiber networks. In particular, we want to understand how these properties are correlated to the network structure. In a first step, we have established rigorous upper-bounds on the elastic moduli and (electric or thermal) conductivity of a network with given density. We also have established necessary and sufficient conditions on the network architecture to reach these bounds. We are currently trying to define an ad-hoc "order parameter" which allows to measure the deviation from these conditions for any network. With help of numerical simulations, we are investigating how the mechanical and transport properties of fiber networks are correlated to this order parameter.

- G. Gurtner and M. Durand, "Structural Properties of Stiff Elastic Networks", EPL 87 24001 (2009).

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