  In practice, physical membranes are exposed to a certain amount of external
strain (tension or compression), due to the environment where they are placed.
As a result, the behavior of the phonon modes of the membrane is modified. We
show that anharmonic effects in stiff two-dimensional membranes are highly
suppressed under the application of tension. For this, we consider the
anharmonic coupling between bending and stretching modes in the self-consistent
screening approximation (SCSA), and compare the obtained height-height
correlation function in the SCSA to the corresponding harmonic propagator. The
elasticity theory results are compared to atomistic Monte Carlo simulations for
a graphene membrane under tension. We find that, while rather high values of
strain are needed to avoid anharmonicity in soft membranes, strain fields less
than 1% are enough to suppress all the anharmonic effects in stiff membranes,
as graphene.

Materials Science;Soft Condensed Matter