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We consider periodic homogenization of hyperelastic models incorporating incompressible behavior via the constraint (u) =1. We show that the 'usual' homogenized integral functional W ₇₎₌ (u) \, dx, where W ₇₎₌ is the standard multicell-formula of non-convex homogenization restricted to volume preserving deformations, yields an upper bound for the -limit as the scale of periodicity tends to zero.
Ruf et al. (Tue,) studied this question.