  We prove a Gamma-convergence result for a family of bending energies defined
on smooth surfaces in $\mathbb{R}^3$ equipped with a director field. The
energies strongly penalize the deviation of the director from the surface unit
normal and control the derivatives of the director. Such type of energies for
example arise in a model for bilayer membranes introduced by Peletier and
R\"oger [Arch. Ration. Mech. Anal. 193 (2009)]. Here we prove in three space
dimensions in the vanishing-tilt limit a Gamma-liminf estimate with respect to
a specific curvature energy. In order to obtain appropriate compactness and
lower semi-continuity properties we use tools from geometric measure theory, in
particular the concept of generalized Gauss graphs and curvature varifolds.
