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 κ.We obtain scaling functions for the behavior of some elastic moduli in the limits of small ∆P = 1 -P, and small δP = P -Pc, where P is an occupation probability of each bond, and Pc is the critical probability at which rigidity percolation occurs.We find good quantitative agreement between effective-medium theory and simulations for both lattices for P close to one.

Locations

• Journal of Physics Condensed Matter - View
• arXiv (Cornell University) - View - PDF
• PubMed - View
• DataCite API - View