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.

Download full text files

Export metadata


Number of document requests

Additional Services

Share in Twitter Search Google Scholar
Author:Manuel Friedrich, Bernd SchmidtGND
Frontdoor URL
Series (Serial Number):Preprints des Instituts für Mathematik der Universität Augsburg (2011-13)
Publishing Institution:Universität Augsburg
Release Date:2011/09/02
Tag:atomares Modell
brittle materials; variational fracture; atomistic models; discrete-to-continuum limits; free discontinuity problems
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