Multiscale boundary conditions in crystalline solids: Theory and application to nanoindentation

E. G. Karpov*, H. Yu, H. S. Park, Wing Kam Liu, Q. Jane Wang, D. Qian

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

44 Scopus citations


This paper presents a systematic approach to treating the interfaces between the localized (fine grain) and peripheral (coarse grain) domains in atomic scale simulations of crystalline solids. Based on Fourier analysis of regular lattices structures, this approach allows elimination of unnecessary atomic degrees of freedom over the coarse grain, without involving an explicit continuum model for the latter. The mathematical formulation involves compact convolution operators that relate displacements of the interface atoms and the adjacent atoms on the coarse grain. These operators are defined by geometry of the lattice structure, and interatomic potentials. Application and performance are illustrated on quasistatic nanoindentation simulations with a crystalline gold substrate. Complete atomistic resolution on the coarse grain is alternatively employed to give the benchmark solutions. The results are found to match well for the multiscale and the full atomistic simulations.

Original languageEnglish (US)
Pages (from-to)6359-6379
Number of pages21
JournalInternational Journal of Solids and Structures
Issue number21
StatePublished - Oct 2006


  • Boundary conditions
  • Crystal structure
  • Molecular dynamics
  • Multiscale simulation
  • Nanoindentation

ASJC Scopus subject areas

  • Modeling and Simulation
  • General Materials Science
  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering
  • Applied Mathematics


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