Multiscale computations of fracture: quantum to continuum

Ted Belytschko

The prediction of the strength of materials from fundamental principles poses a formidable challenge. Since bond breaking is involved, a first principles attack on the problem requires quantum mechanical modeling at the bond breaking level. However, it has become apparent that even at the nanoscale, strength seems to be dominated by defects in the specimen. To study such defects in terms of basic physics, quantum mechanics is usually necessary to model bond breaking. However, to account for defects, the models must be substantially larger than can be treated by quantum mechanics with modest computational power. Here a coupled method for quantum/molecular/continuum mechanics is described. A method for coupling quantum mechanics with molecular mechanics is summarized, as well as methods for coupling molecular mechanics with continuum mechanics [1].

The coupled method is then applied to the analysis of the strength of crystalline carbon nanotubes and nanoscale graphene sheets with defects. Both holes and slitlike defects that are similar to cracks are considered. The results show that the strength in crystalline carbon diminishes rapidly with flaw size and in fact agrees quite closely with the Griffith formula when the surface energy is obtained by a quantum calculation. Computations of the strength of amorphous carbon nanostructures have also been made [2]. The environment-independent interatomic potential of Marks, which is well suited to amorphous carbon, is used. These manifest much less decrease in strength with increasing flaw size, indicative of a flaw tolerance.

1. R. Khare, S.L. Mielke, J.T. Paci, S. Zhang, R. Ballarini, G.C. Schatz, and T. Belytschko, "Coupled quantum mechanical/molecular mechanical modeling of the fracture of defective carbon nanotubes and grapheme sheets," Physical Review B, v. 75, issue 7, article number 075412, 2007.
2. Q. Lu, N. Marks, G.C. Schatz, and T. Belytschko, "Nanoscale fracture of tetrahedral amorphous carbon by molecular dynamics: Flaw size insensitivity," Physical Review B, v. 77, issue 1, article number 014109, 2008.