Effective Medium Theory of Filamentous Triangular Lattice

Details Effective Medium Theory of Filamentous Triangular Lattice Effective Medium Theory of Filamentous Triangular Lattice

2011-11-07

arxiv.org/abs/1111.1751v1

Physics

Condensed Matter

Soft Condensed Matter

13 pages, 8 figures

Scientific paper

We present a new effective medium theory that can include bending as well as stretching forces, and we use it to calculate mechanical response of a diluted filamentous triangular lattice. In this lattice, bonds are central-force springs, and there are bending forces between neighboring bonds on the same filament. We investigate the diluted lattice in which each bond is present with a probability $p$. We find a rigidity threshold independent of filament bending rigidity at $p_b \simeq 0.56$ and a crossover characterizing bending-, stretching-, and bend-stretch coupled elastic regimes controlled by the central-force isostatic point at $p_{\textrm{CF}}=2/3$ of the lattice when bending forces vanish.

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