## Department of Physics Papers

#### Document Type

Journal Article

#### Date of this Version

4-9-2013

#### Abstract

The diluted kagome lattice, in which bonds are randomly removed with probability 1−p, 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=p_{b}≈0.605 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 p_{b}, that match simulations with no adjustable parameters near p=1. The affine response as p→1 is identified with the approach to a state with sample-crossing straight filaments treated as elastic rods.

#### Recommended Citation

Mao, X., Stenull, O., & Lubensky, T. C. (2013). Elasticity of a filamentous kagome lattice. Retrieved from https://repository.upenn.edu/physics_papers/283

**Date Posted:** 09 May 2013

This document has been peer reviewed.

## Comments

Mao, X., Stenull, O., & Lubensky, T. C. (2013). Elasticity of a filamentous kagome lattice.

Physical Review E, 87(4), 042602. doi: 10.1103/PhysRevE.87.042602©2013 American Physical Society