  We consider periodic homogenization of hyperelastic models incorporating
incompressible behavior via the constraint $\det(\nabla u)=1$. We show that the
'usual' homogenized integral functional $\int W_{\rm hom}(\nabla u)\,dx$, where
$W_{\rm hom}$ is the standard multicell-formula of non-convex homogenization
restricted to volume preserving deformations, yields an upper bound for the
$\Gamma$-limit as the scale of periodicity tends to zero.
