A coupled quantum/continuum mechanics study of graphene fracture

Mei Xu, Alireza Tabarraei, Jeffrey T. Paci, Jay Oswald, Ted Belytschko

Research output: Contribution to journalArticlepeer-review

87 Scopus citations


A new technique is presented to study fracture in nanomaterials by coupling quantum mechanics (QM) and continuum mechanics (CM). A key new feature of this method is that broken bonds are identified by a sharp decrease in electron density at the bond midpoint in the QM model. As fracture occurs, the crack tip position and crack path are updated from the broken bonds in the QM model. At each step in the simulation, the QM model is centered on the crack tip to adaptively follow the path. This adaptivity makes it possible to trace paths with complicated geometries. The method is applied to study the propagation of cracks in graphene which are initially perpendicular to zigzag and armchair edges. The simulations demonstrate that the growth of zigzag cracks is self-similar whereas armchair cracks advance in an irregular manner. The critical stress intensity factors for graphene were found to be 4.21 MPa √ m for zigzag cracks and 3.71 MPa √ m for armchair cracks, which is about 10% of that for steel.

Original languageEnglish (US)
Pages (from-to)163-173
Number of pages11
JournalInternational Journal of Fracture
Issue number2
StatePublished - Feb 2012


  • Adaptivity
  • Fracture
  • Graphene
  • Multiscale

ASJC Scopus subject areas

  • Computational Mechanics
  • Modeling and Simulation
  • Mechanics of Materials


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