  A justification of heterogeneous membrane models as zero-thickness limits of
a cylindral three-dimensional heterogeneous nonlinear hyperelastic body is
proposed in the spirit of Le Dret & Raoult. Specific characterizations of the
2D elastic energy are produced. As a generalization of Bouchitt\'e, Fonseca &
Mascarenhas, the case where external loads induce a density of bending moment
that produces a Cosserat vector field is also investigated. Throughout, the
3D-2D dimensional reduction is viewed as a problem of $\Gamma$-convergence of
the elastic energy, as the thickness tends to zero.
