  We provide universal formulae for the limiting stretching and bending
energies of triangulated membrane networks endowed with nearest neighbor bond
potentials and cosine-type dihedral angle potentials. The given formulae
account for finite elasticity and solve some deficiencies of earlier results
for Helfrich-type bending energies, due to shape-dependence and sensitivity to
mesh distortion effects of the limiting elastic coefficients. We also provide
the entire set of the elastic coefficients characterizing the limiting response
of the examined networks, accounting for full bending-stretching coupling. We
illustrate the effectiveness of the proposed formulae by way of example, on
examining the special cases of cylindrical and spherical networks covered with
equilateral triangles, and discussing possible strategies for the experimental
characterization of selected elastic moduli.
