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Research Article | Open Access

An atomistic derivation of von-Kármán plate theory

Heriot-Watt University, United Kingdom
Universität Augsburg, Germany
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Abstract

We derive von-Kármán plate theory from three dimensional, purely atomistic models with classical particle interaction. This derivation is established as a Γ-limit when considering the limit where the interatomic distance ε as well as the thickness of the plate h tend to zero. In particular, our analysis includes the ultrathin case where ε ∼ h, leading to a new von-Kármán plate theory for finitely many layers.

Keywords

Discrete to continuumgamma-convergencedimension reductionelastic platesvon-Kármán plate theory
CLC number: Primary: 49J45, 70C20, 74K20

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Networks and Heterogeneous Media
Volume 17 Issue 4,
August 2022
Pages 613-644
DOI: 10.3934/nhm.2022019

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Braun J, Schmidt B. An atomistic derivation of von-Kármán plate theory. Networks and Heterogeneous Media, 2022, 17(4): 613-644. https://doi.org/10.3934/nhm.2022019

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Received: 01 July 2021
Revised: 01 February 2022
Published: 15 August 2022
©2022 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)