Stiffest Elastic Networks

Abstract

The rigidity of a network of elastic beams crucially depends on the specific details of its structure. We show both numerically and theoretically that there is a class of isotropic networks which are stiffer than any other isotropic network with same density. The elastic moduli of these \textit{stiffest elastic networks} are explicitly given. They constitute upper-bounds which compete or improve the well-known Hashin-Shtrikman bounds. We provide a convenient set of criteria (necessary and sufficient conditions) to identify these networks, and show that their displacement field under uniform loading conditions is affine down to the microscopic scale. Finally, examples of such networks with periodic arrangement are presented, in both two and three dimensions.

References in corpus (10)

• Elasticity of Stiff Polymer Networks
• Deformation of crosslinked semiflexible polymer networks
• Distinct regimes of elastic response and deformation modes of cross-linked cytoskeletal and semiflexible polymer networks
• Isostaticity, auxetic response, surface modes, and conformal invariance in twisted kagome lattices
• Nonaffine Correlations in Random Elastic Media
• Nonaffine rubber elasticity for stiff polymer networks
• Visualizing the strain field in semiflexible polymer networks: strain fluctuations and nonlinear rheology of F-actin gels
• Stiff Polymers, Foams and Fiber Networks
• Optimizing transport in a homogeneous network
• Structural Properties of Stiff Elastic Networks

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