From Atomistic to Continuum Theory for Brittle Materials: A Two-Dimensional Model Problem
- A two-dimensional atomic mass spring system is investigated for critical fracture loads and its crack path geometry. We rigorously prove that in the discrete-to-continuum limit, the minimal energy leads to a universal cleavage law and energy minimizers are either homogeneous elastic deformations or configurations that are cracked along specific crystallographic hyperplanes. Furthermore, we identify an effective continuum model through Gamma-convergence.
| Author: | Manuel Friedrich, Bernd SchmidtGND |
|---|---|
| URN: | urn:nbn:de:bvb:384-opus4-12484 |
| Frontdoor URL | https://opus.bibliothek.uni-augsburg.de/opus4/1564 |
| Series (Serial Number): | Preprints des Instituts für Mathematik der Universität Augsburg (2011-13) |
| Type: | Preprint |
| Language: | English |
| Date of Publication (online): | 2011/09/02 |
| Year of first Publication: | 2011 |
| Publishing Institution: | Universität Augsburg |
| Release Date: | 2011/09/02 |
| Tag: | atomares Modell atomistic models; brittle materials; discrete-to-continuum limits; free discontinuity problems; variational fracture |
| GND-Keyword: | Bruchmechanik; Rissausbreitung; Mathematische Modellierung; Poröser Stoff; Variationsrechnung |
| 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 |
