A continuum model for brittle nanowires derived from an atomistic description by Γ-convergence

  • Starting from a particle system with short-range interactions, we derive a continuum model for the bending, torsion, and brittle fracture of inextensible rods moving in three-dimensional space. As the number of particles tends to infinity, it is assumed that the rod's thickness is of the same order as the interatomic distance. Fracture energy in the Γ-limit is expressed by an implicit cell formula, which covers different modes of fracture, including (complete) cracks, folds and torsional cracks. In special cases, the cell formula can be significantly simplified. Our approach applies e.g. to atomistic systems with Lennard-Jones-type potentials and is motivated by the research of ceramic nanowires.

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Author:Bernd SchmidtGND, Jiří ZemanORCiDGND
Frontdoor URLhttps://opus.bibliothek.uni-augsburg.de/opus4/101058
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