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We use numerical simulations and an effective-medium theory to study therigidity percolation transition of the honeycomb and diamond lattices when weakbond-bending forces are included. We use a rotationally invariant bond-bendingpotential, which, in contrast to the Keating potential, does not involve anystretching. As a result, the bulk modulus does not depend on the bendingstiffness $\kappa$. We obtain scaling functions for the behavior of someelastic 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 $\mathcal{P}_c$ isthe critical probability at which rigidity percolation occurs. We find goodquantitative agreement between effective-medium theory and simulations for bothlattices for $\mathcal{P}$ close to one.

Elasticity of randomly diluted honeycomb and diamond lattices with bending forces