# On the derivation of homogenized bending plate model

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## Abstract

We derive, via simultaneous homogenization and dimension reduction, the \(\Gamma \)-limit for thin elastic plates of thickness \(h\) whose energy density oscillates on a scale \(\varepsilon (h)\) such that \( \varepsilon (h)^2 \ll h\ll \varepsilon (h)\). We consider the energy scaling that corresponds to Kirchhoff’s nonlinear bending theory of plates.

## Mathematics Subject Classification

35B27 49J45 74E30 74Q05## Notes

### Acknowledgments

The work on this paper was mainly done while the author was affiliated with Peter Hornung’s group in Max Planck Institute for Mathematics in the Sciences in Leipzig, Germany. The author was supported by Deutsche Forschungsgemeinschaft grant no. HO-4697/1-1.

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