A bending-torsion theory for thin and ultrathin rods as a Γ-limit of atomistic models

  • The purpose of this note is to establish two continuum theories for the bending and torsion of inextensible rods as Γ-limits of 3D atomistic models. In our derivation we study simultaneous limits of vanishing rod thickness h and interatomic distance ε. First, we set up a novel theory for ultrathin rods composed of finitely many atomic fibres (ε∼h), which incorporates surface energy and new discrete terms in the limiting functional. This can be thought of as a contribution to the mechanical modelling of nanowires. Second, we treat the case where ε≪h and recover a nonlinear rod model − the modern version of Kirchhoff's rod theory.

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Author:Bernd SchmidtGND, Jiří ZemanORCiDGND
Frontdoor URLhttps://opus.bibliothek.uni-augsburg.de/opus4/101059
Parent Title (English):arXiv
Year of first Publication:2022
Publishing Institution:Universität Augsburg
Release Date:2023/01/19
Institutes:Mathematisch-Naturwissenschaftlich-Technische Fakultät
Mathematisch-Naturwissenschaftlich-Technische Fakultät / Institut für Mathematik
Mathematisch-Naturwissenschaftlich-Technische Fakultät / Institut für Mathematik / Lehrstuhl für Nichtlineare Analysis
Dewey Decimal Classification:5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik
Licence (German):Deutsches Urheberrecht