An atomistic derivation of von-Kármán plate theory

Julian Braun; Bernd Schmidt

doi:10.3934/nhm.2022019

Article Contents

2022, Volume 17, Issue 4: 613-644. Doi: 10.3934/nhm.2022019

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An atomistic derivation of von-Kármán plate theory

Julian Braun^1, , and
Bernd Schmidt^2,

1.
Heriot-Watt University, United Kingdom
2.
Universität Augsburg, Germany

^*Corresponding author: Julian Braun
^*Corresponding author: Julian Braun

Received: July 2021

Revised: February 2022

Early access: April 2022

Published: August 2022

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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 $ \Gamma $-limit when considering the limit where the interatomic distance $ \varepsilon $ as well as the thickness of the plate $ h $ tend to zero. In particular, our analysis includes the ultrathin case where $ \varepsilon \sim h $, leading to a new von-Kármán plate theory for finitely many layers.

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Mathematics Subject Classification: Primary: 49J45, 70C20, 74K20.

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