On the simultaneous homogenization and dimension reduction in elasticity and locality of \(\varGamma\)-closure. (English) Zbl 1370.74018
Summary: We provide a framework for simultaneous homogenization and dimension reduction in the setting of linearized elasticity as well as non-linear elasticity for the derivation of homogenized von Kármán plate and bending rod models. The framework encompasses even perforated domains and domains with oscillatory boundary, provided that the corresponding extension operator can be constructed. Locality property of \(\varGamma\)-closure is established, i.e. every energy density obtained by the homogenization process can be in almost every point obtained as the limit of periodic energy densities.
MSC:
| 74B05 | Classical linear elasticity |
| 74B20 | Nonlinear elasticity |
| 74E30 | Composite and mixture properties |
| 74K20 | Plates |
| 74Q05 | Homogenization in equilibrium problems of solid mechanics |
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