An atomistic derivation of von-Kármán plate theory

Julian Braun*, Bernd Schmidt

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

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.

Original languageEnglish
Pages (from-to)613-644
Number of pages32
JournalNetworks and Heterogeneous Media
Volume17
Issue number4
Early online date1 Apr 2022
DOIs
Publication statusPublished - Aug 2022

Keywords

  • dimension reduction
  • Discrete to continuum
  • elastic plates
  • gamma-convergence
  • von-Kármán plate theory

ASJC Scopus subject areas

  • Statistics and Probability
  • Engineering(all)
  • Computer Science Applications
  • Applied Mathematics

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