Commutativity and non-commutativity of limits in the nonlinear bending theory for prestrained microheterogeneous plates
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| Main Authors: | , , , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866911146299097088 |
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| author | Boehnlein, Klaus Bouck, Lucas Neukamm, Stefan Padilla-Garza, David Richter, Kai |
| author_facet | Boehnlein, Klaus Bouck, Lucas Neukamm, Stefan Padilla-Garza, David Richter, Kai |
| contents | In this paper we study the derivation of nonlinear bending models for prestrained elastic plates from three-dimensional non-linear elasticity via homogenization and dimension reduction. We compare effective models obtained by either simultaneously or consecutively passing to the $Γ$-limits as the thickness $h\ll1$ and the size of the material microstructure $\e\ll1$ vanish. In the regime $\e\ll h$ we show that the consecutive and simultaneous limit are equivalent, and also analyze the rate of convergence. In contrast, we observe that there are several different limit models in the case $h\ll \e$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2410_15679 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Commutativity and non-commutativity of limits in the nonlinear bending theory for prestrained microheterogeneous plates Boehnlein, Klaus Bouck, Lucas Neukamm, Stefan Padilla-Garza, David Richter, Kai Analysis of PDEs 49S05 74K20 74Q05 In this paper we study the derivation of nonlinear bending models for prestrained elastic plates from three-dimensional non-linear elasticity via homogenization and dimension reduction. We compare effective models obtained by either simultaneously or consecutively passing to the $Γ$-limits as the thickness $h\ll1$ and the size of the material microstructure $\e\ll1$ vanish. In the regime $\e\ll h$ we show that the consecutive and simultaneous limit are equivalent, and also analyze the rate of convergence. In contrast, we observe that there are several different limit models in the case $h\ll \e$. |
| title | Commutativity and non-commutativity of limits in the nonlinear bending theory for prestrained microheterogeneous plates |
| topic | Analysis of PDEs 49S05 74K20 74Q05 |
| url | https://arxiv.org/abs/2410.15679 |