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].…
Author: | Laura Lauerbach, Stefan Neukamm, Mathias Schäffner, Anja Schlömerkemper |
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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): | CC BY: Creative-Commons-Lizenz: Namensnennung 4.0 International |