Elasticity of randomly diluted honeycomb and diamond lattices with bending forces

Abstract

We use numerical simulations and an effective-medium theory to study the rigidity percolation transition of the honeycomb and diamond lattices when weak bond-bending forces are included. We use a rotationally invariant bond-bending potential, which, in contrast to the Keating potential, does not involve any stretching. As a result, the bulk modulus does not depend on the bending stiffness $\kappa$. We obtain scaling functions for the behavior of some elastic moduli in the limits of small $\Delta \mathcal{P}=1-\mathcal{P}$, and small $\delta \mathcal{P}=\mathcal{P}-{\mathcal{P}}_c$, where $\mathcal{P}$ is an occupation probability of each bond, and ${\mathcal{P}}_c$ is the critical probability at which rigidity percolation occurs. We find good quantitative agreement between effective-medium theory and simulations for both lattices for $\mathcal{P}$ close to one.

10 pages, 9 figures

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• Modeling semiflexible polymer networks
• Elasticity of Stiff Polymer Networks
• Effective medium theory of semiflexible filamentous networks
• Elasticity and Response in Nearly Isostatic Periodic Lattices
• Elasticity of Filamentous Kagome Lattice
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Cited by in corpus (4)

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