A derivation of the time dependent von K\'arm\'an equations from atomistic models

David Buchberger; Bernd Schmidt

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arXiv · 2411.10233

A derivation of the time dependent von K\'arm\'an equations from atomistic models

David Buchberger·Bernd Schmidt

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Abstract

We derive the time-dependent von K\'arm\'an 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 K\'arm\'an 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 $\eps \sim h$.

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David Buchberger, Bernd Schmidt. 2024-11-15. A derivation of the time dependent von K\'arm\'an equations from atomistic models. https://arxiv.org/abs/2411.10233

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