Abstract
The diluted kagome lattice, in which bonds are randomly removed with probability , 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 and bending modulus , are used to study the elasticity of this lattice as functions of and . At , elastic response is purely affine, and the macroscopic elastic modulus is independent of . When , the lattice undergoes a first-order rigidity-percolation transition at . When , decreases continuously as decreases below one, reaching zero at a continuous rigidity-percolation transition at that is the same for all nonzero values of . The effective-medium theories predict scaling forms for , which exhibit crossover from bending-dominated response at small to stretching-dominated response at large near both and , that match simulations with no adjustable parameters near . The affine response as is identified with the approach to a state with sample-crossing straight filaments treated as elastic rods.
3 More- Received 4 January 2013
DOI:https://doi.org/10.1103/PhysRevE.87.042602
©2013 American Physical Society