  Twisted graphene layers produce a moir\'e pattern (MP) structure with a
predetermined wavelength for given twist angle. However, predicting the
membrane corrugation amplitude for any angle other than pure AB-stacked or
AA-stacked graphene is impossible using first-principles density functional
theory (DFT) due to the large supercell. Here, within elasticity theory we
define the MP structure as the minimum energy configuration, thereby leaving
the height amplitude as the only unknown parameter. The latter is determined
from DFT calculations for AB and AA stacked bilayer graphene in order to
eliminate all fitting parameters. Excellent agreement with scanning tunneling
microscopy (STM) results across multiple substrates is reported as function of
twist angle.

Mesoscale and Nanoscale Physics