A temperature equation for coupled atomistic/continuum simulations

Harold S. Park*, Eduard G. Karpov, Wing Kam Liu

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

54 Scopus citations


We present a simple method for calculating a continuum temperature field directly from a molecular dynamics (MD) simulation. Using the idea of a projection matrix previously developed for use in the bridging scale, we derive a continuum temperature equation which only requires information that is readily available from MD simulations, namely the MD velocity, atomic masses and Boltzmann constant. As a result, the equation is valid for usage in any coupled finite element (FE)/MD simulation. In order to solve the temperature equation in the continuum where an MD solution is generally unavailable, a method is utilized in which the MD velocities are found at arbitrary coarse scale points by means of an evolution function. The evolution function is derived in closed form for a 1D lattice, and effectively describes the temporal and spatial evolution of the atomic lattice dynamics. It provides an accurate atomistic description of the kinetic energy dissipation in simulations, and its behavior depends solely on the atomic lattice geometry and the form of the MD potential. After validating the accuracy of the evolution function to calculate the MD variables in the coarse scale, two 1D examples are shown, and the temperature equation is shown to give good agreement to MD simulations.

Original languageEnglish (US)
Pages (from-to)1713-1732
Number of pages20
JournalComputer Methods in Applied Mechanics and Engineering
Issue number17-20
StatePublished - May 7 2004


  • Bridging scale
  • Coupling methods
  • Finite elements
  • Finite temperature
  • Lattice evolution function
  • Molecular dynamics
  • Multiple scale simulations

ASJC Scopus subject areas

  • Computational Mechanics
  • Mechanics of Materials
  • Mechanical Engineering
  • General Physics and Astronomy
  • Computer Science Applications


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