Elasticity of a filamentous kagome lattice

Xiaoming Mao, Olaf Stenull, and T. C. Lubensky
Phys. Rev. E 87, 042602 – Published 9 April 2013

Abstract

The diluted kagome lattice, in which bonds are randomly removed with probability 1p, consists of straight lines that intersect at points with a maximum coordination number of 4. If lines are treated as semiflexible polymers and crossing points are treated as cross-links, this lattice provides a simple model for two-dimensional filamentous networks. Lattice-based effective-medium theories and numerical simulations for filaments modeled as elastic rods, with stretching modulus μ and bending modulus κ, are used to study the elasticity of this lattice as functions of p and κ. At p=1, elastic response is purely affine, and the macroscopic elastic modulus G is independent of κ. When κ=0, the lattice undergoes a first-order rigidity-percolation transition at p=1. When κ>0, G decreases continuously as p decreases below one, reaching zero at a continuous rigidity-percolation transition at p=pb0.605 that is the same for all nonzero values of κ. The effective-medium theories predict scaling forms for G, which exhibit crossover from bending-dominated response at small κ/μ to stretching-dominated response at large κ/μ near both p=1 and pb, that match simulations with no adjustable parameters near p=1. The affine response as p1 is identified with the approach to a state with sample-crossing straight filaments treated as elastic rods.

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  • Received 4 January 2013

DOI:https://doi.org/10.1103/PhysRevE.87.042602

©2013 American Physical Society

Authors & Affiliations

Xiaoming Mao1,2, Olaf Stenull1, and T. C. Lubensky1

  • 1Department of Physics and Astronomy, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
  • 2Department of Physics, University of Michigan, Ann Arbor, Michigan 48109-1040, USA

See Also

Effective-medium theory of a filamentous triangular lattice

Xiaoming Mao, Olaf Stenull, and T. C. Lubensky
Phys. Rev. E 87, 042601 (2013)

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Vol. 87, Iss. 4 — April 2013

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