A derivation of the time dependent von Kármán equations from atomistic models
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866912120510087168 |
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| author | Buchberger, David Schmidt, Bernd |
| author_facet | Buchberger, David Schmidt, Bernd |
| contents | We derive the time-dependent von Kármán plate equations from three dimensional, purely atomistic particle models. In particular, we prove that a thin structure of interacting particles whose dynamics is governed by Newton's laws of motion is effectively described by the von Kármán equations in the limit of vanishing interatomic distance $\eps$ and vanishing plate thickness $h$. While the classical plate equations are obtained for $\eps \ll h \ll 1$, we find new plate equations for finitely many layers in the ultrathin case $\eps \sim h$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2411_10233 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A derivation of the time dependent von Kármán equations from atomistic models Buchberger, David Schmidt, Bernd Analysis of PDEs 74K20, 35L70, 35Q70 We derive the time-dependent von Kármán plate equations from three dimensional, purely atomistic particle models. In particular, we prove that a thin structure of interacting particles whose dynamics is governed by Newton's laws of motion is effectively described by the von Kármán equations in the limit of vanishing interatomic distance $\eps$ and vanishing plate thickness $h$. While the classical plate equations are obtained for $\eps \ll h \ll 1$, we find new plate equations for finitely many layers in the ultrathin case $\eps \sim h$. |
| title | A derivation of the time dependent von Kármán equations from atomistic models |
| topic | Analysis of PDEs 74K20, 35L70, 35Q70 |
| url | https://arxiv.org/abs/2411.10233 |