Molecular dynamics boundary conditions for regular crystal lattices

Gregory J. Wagner, Eduard G. Karpov, Wing Kam Liu*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

85 Scopus citations


We present a method for deriving molecular dynamics boundary conditions for use in multiple scale simulations that can be applied at a planar boundary for any solid that has a periodically repeating crystal lattice. The method is based on a linearization in the vicinity of the boundary, and utilizes a Fourier and Laplace transforms in space and time to eliminate the degrees of freedom associated with atoms outside the boundary. This method is straightforward to implement numerically, and thus can be automated for a general crystal lattice. We show that this method reproduces the known kernel for a 1D linear chain, and apply the approach to obtain the damping kernel matrices for two real crystal lattices: the graphene and diamond structures of carbon.

Original languageEnglish (US)
Pages (from-to)1579-1601
Number of pages23
JournalComputer Methods in Applied Mechanics and Engineering
Issue number17-20
StatePublished - May 7 2004


  • Boundary conditions
  • Generalized Langevin equation
  • Molecular dynamics
  • Multiple scale simulations

ASJC Scopus subject areas

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


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