Coupled quantum mechanical/molecular mechanical modeling of the fracture of defective carbon nanotubes and graphene sheets

By R. Khare, S. L. Mielke, Jeffrey T. Paci, Sulin Zhang, R. Ballarini, George C. Schatz, Ted Belytschko. 2007

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Hybrid atomistic simulation methods for materials systems (2009, methodology): “elastic constants [7, 11] and the Einstein oscillator frequencies,”
Effects of functional groups on the mechanical and wrinkling properties of graphene sheets (2010, background): “[25] Khare R, Mielke SL, Paci JT, Zhang S, Ballarini R, Schatz GC, et al.”
Coarse‐graining of multiscale crack propagation (2010, background): “[20], the atomistic and quantum domains are embedded in a continuum domain, and in Xiao and Belytschko [21] and Wagner and Liu [22], atomistic domains are embedded in continuum domains.”
A review on mechanics and mechanical properties of 2D materials—Graphene and beyond (2016, background): “It has been shown that the calculated fracture toughness of graphene is higher than its surface energy [157] due to the discrete lattice trapping effect [166,167].”
Fracture of graphene: a review (2015, methodology): “…0.13 J/m2 J-integral for MM simulations (Jin and Yuan 2005) SG 10.8−15.8 J/m2 J-integral for coupled quantum/molecular mechanics and MM simulations (Khare et al. 2007) SG 10.68∗ J/m2 K-field loading for MM simulations (Terdalkar et al. 2010) SG 4.21a, 3.71z MPa m1/2 K-field loading for coupled…”