  We investigate the electromechanical coupling in 2d materials. For
non-Bravais lattices, we find important corrections to the standard macroscopic
strain - microscopic atomic-displacement theory. We put forward a general and
systematic approach to calculate strain-displacement relations for several
classes of 2d materials. We apply our findings to graphene as a study case, by
combining a tight binding and a valence force-field model to calculate
electronic and mechanical properties of graphene nanoribbons under strain. The
results show good agreement with the predictions of the Dirac equation coupled
to continuum mechanics. For this long wave-limit effective theory, we find that
the strain-displacement relations lead to a renormalization correction to the
strain-induced pseudo-magnetic fields. Implications for nanomechanical
properties and electromechanical coupling in 2d materials are discussed.
