Bridging scale methods for nanomechanics and materials

Wing Kam Liu, Harold S. Park, Dong Qian, Eduard G. Karpov, Hiroshi Kadowaki, Gregory J. Wagner

Research output: Contribution to journalArticlepeer-review

125 Scopus citations


Inspired by the pioneering work of Professor T.J.R. Hughes on the variational multi-scale method, this document summarizes recent developments in multiple-scale modeling using a newly developed technique called the bridging scale. The bridging scale consists of a two-scale decomposition in which the coarse scale is simulated using continuum methods, while the fine scale is simulated using atomistic approaches. The bridging scale offers unique advantages in that the coarse and fine scales evolve on separate time scales, while the high frequency waves emitted from the fine scale are eliminated using lattice impedance techniques. Recent advances in extending the bridging scale to quantum mechanical/continuum coupling are briefly described. The method capabilities are demonstrated via quasistatic nanotube bending, dynamic crack propagation and dynamic shear banding.

Original languageEnglish (US)
Pages (from-to)1407-1421
Number of pages15
JournalComputer Methods in Applied Mechanics and Engineering
Issue number13-16
StatePublished - Feb 15 2006


  • Bridging scale
  • Carbon nanotubes
  • Coupling methods
  • Dynamic fracture
  • Finite elements
  • Finite temperature
  • Generalized Langevin equation
  • Molecular dynamics
  • Multiple scale simulations
  • Quantum mechanical/continuum coupling

ASJC Scopus subject areas

  • Computational Mechanics
  • Mechanics of Materials
  • Mechanical Engineering
  • Physics and Astronomy(all)
  • Computer Science Applications


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