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 |
|---|---|
| URN: | urn:nbn:de:bvb:384-opus4-1010595 |
| Frontdoor URL | https://opus.bibliothek.uni-augsburg.de/opus4/101059 |
| Parent Title (English): | arXiv |
| Type: | Preprint |
| Language: | English |
| Year of first Publication: | 2022 |
| Publishing Institution: | Universität Augsburg |
| Release Date: | 2023/01/19 |
| Issue: | arXiv:2208.04199 |
| DOI: | https://doi.org/10.48550/arXiv.2208.04199 |
| 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 |
