MiS Preprint Repository

We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV ( that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint

Homogenization of the nonlinear bending theory for plates

Stefan Neukamm and Heiner Olbermann


We carry out the spatially periodic homogenization of Kirchhoff’s plate theory. The derivation is rigorous in the sense of $\Gamma$-convergence. In contrast to what one naturally would expect, our result shows that the limiting functional is not simply a quadratic functional of the second fundamental form of the deformed plate as it is the case in Kirchhoff’s plate theory. It turns out that the limiting functional discriminates between whether the deformed plate is locally shaped like a "cylinder" or not. For the derivation we investigate the oscillatory behavior of sequences of second fundamental forms associated with isometric immersions of class $W^{2,2}$, using two-scale convergence. This is a non-trivial task, since one has to treat two-scale convergence in connection with a nonlinear differential constraint.

MSC Codes:
35B27, 74Q15, 74K20
homogenization, Kirchhoff plate theory, two-scale convergence, nonlinear differential constraint

Related publications

2015 Repository Open Access
Stefan Neukamm and Heiner Olbermann

Homogenization of the nonlinear bending theory for plates

In: Calculus of variations and partial differential equations, 53 (2015) 3, pp. 719-753