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Continuum Limit and Homogenization of Stochastic and Periodic Discrete Systems – Fracture in Composite Materials

Please always quote using this URN: urn:nbn:de:bvb:20-opus-211835
  • The limiting behaviour of a one‐dimensional discrete system is studied by means of Γ‐convergence. We consider a toy model of a chain of atoms. The interaction potentials are of Lennard‐Jones type and periodically or stochastically distributed. The energy of the system is considered in the discrete to continuum limit, i.e. as the number of atoms tends to infinity. During that limit, a homogenization process takes place. The limiting functional is discussed, especially with regard to fracture. Secondly, we consider a rescaled version of theThe limiting behaviour of a one‐dimensional discrete system is studied by means of Γ‐convergence. We consider a toy model of a chain of atoms. The interaction potentials are of Lennard‐Jones type and periodically or stochastically distributed. The energy of the system is considered in the discrete to continuum limit, i.e. as the number of atoms tends to infinity. During that limit, a homogenization process takes place. The limiting functional is discussed, especially with regard to fracture. Secondly, we consider a rescaled version of the problem, which yields a limiting energy of Griffith's type consisting of a quadratic integral term and a jump contribution. The periodic case can be found in [8], the stochastic case in [6,7].show moreshow less

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Metadaten
Author: Laura Lauerbach, Stefan Neukamm, Mathias Schäffner, Anja Schlömerkemper
URN:urn:nbn:de:bvb:20-opus-211835
Document Type:Journal article
Faculties:Fakultät für Mathematik und Informatik / Institut für Mathematik
Language:English
Parent Title (English):Proceedings in Applied Mathematics & Mechanics
Year of Completion:2019
Volume:19
Issue:1
Pagenumber:e201900070
Source:Proceedings in Applied Mathematics & Mechanics 2019, 19(1):e201900070. DOI: 10.1002/pamm.201900070
DOI:https://doi.org/10.1002/pamm.201900070
Dewey Decimal Classification:5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik
Tag:continuum limit; discrete systems; homogenization
Release Date:2020/09/22
Licence (German):License LogoCC BY: Creative-Commons-Lizenz: Namensnennung 4.0 International