Poisson's ratio in composite elastic media with rigid rods

Abstract

We study the elastic response of composites of rods embedded in elastic media. We calculate the micro-mechanical response functions, and bulk elastic constants as functions of rod density. We find two fixed points for Poisson's ratio with respect to the addition of rods in 3D composites: there is an unstable fixed point for Poisson's ratio=1/2 (an incompressible system) and a stable fixed point for Poisson's ratio=1/4 (a compressible system). We also derive an approximate expression for the elastic constants for arbitrary rod density that yields exact results for both low and high density. These results may help to explain recent experiments [Physical Review Letters 102, 188303 (2009)] that reported compressibility for composites of microtubules in F-actin networks.

4 pages, 4 figures, to appear in Phys. Rev. Lett

References in corpus (10)

• Nonlinear Elasticity in Biological Gels
• The origin of stiffening in cross-linked semiflexible networks
• 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
• One- and two-particle microrheology
• Entanglement, elasticity and viscous relaxation of actin solutions
• Nonlinear elasticity of composite networks of stiff biopolymers with flexible linkers
• Visualizing the strain field in semiflexible polymer networks: strain fluctuations and nonlinear rheology of F-actin gels
• Effective medium theory of semiflexible filamentous networks

Cited by in corpus (5)

• Biopolymers: life's mechanical scaffolds
• Redundancy and cooperativity in the mechanics of compositely crosslinked filamentous networks
• Synergistic interactions between DNA and actin trigger emergent viscoelastic behavior
• Mechanics and force transmission in soft composites of rods in elastic gels
• Nonlinear Poisson effect in affine semiflexible polymer networks