Upper bounds for the homogenization problem in nonlinear elasticity: the incompressible case
Matthias Ruf, Mathias Schäffner · arXiv (Cornell University) · 2024
We consider periodic homogenization of hyperelastic models incorporating incompressible behavior via the constraint $\det( abla u)=1$. We show that the 'usual' homogenized integral functional $\int W_{\rm hom}( abla u)\,dx$, where $W_{\rm hom}$ is the standard multicell-formula of non-convex homogenization restricted to volume preserving deformations, yields an upper bound for the $Γ$-limit as the scale of periodicity tends to zero.