title: 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 ΔP = 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.
authors.affiliation: Laboratory of Atomic and Solid State Physics, Cornell University, Ithaca, NY, USA. Institute of Physics, University of São Paulo, São Paulo, SP, Brazil.
authors.forename: Danilo B
authors.initials: DB
authors.lastname: Liarte
authors.forename: O
authors.initials: O
authors.lastname: Stenull
authors.forename: Xiaoming
authors.initials: X
authors.lastname: Mao
authors.forename: T C
authors.initials: TC
authors.lastname: Lubensky