  We present a simple analytical approach to study anharmonic effects in single
layer, bilayer, and multilayer graphene. The coupling between in plane and out
of plane modes leads to negative Gr\"uneisen coefficients and negative thermal
expansion. The value of the thermal expansion coefficient depends on the
coupling to the substrate. The bending rigidity in bilayer graphene shows a
crossover between a long wavelength regime where its value is determined by the
in plane elastic properties and a short wavelength regime where its value
approaches twice that of a single layer.
