A Lagrangian-based continuum homogenization approach applicable to molecular dynamics simulations

P. C. Andia, F. Costanzo, G. L. Gray

Research output: Contribution to journalArticlepeer-review

12 Scopus citations


The continuum notions of effective mechanical quantities as well as the conditions that give meaningful deformation processes for homogenization problems with large deformations are reviewed. A continuum homogenization model is presented and recast as a Lagrangian-based approach for heterogeneous media that allows for an extension to discrete systems simulated via molecular dynamics (MD). A novel constitutive relation for the effective stress is derived so that the proposed Lagrangian-based approach can be used for the determination of the "stress-deformation" behavior of particle systems. The paper is concluded with a careful comparison between the proposed method and the Parrinello-Rahman approach to the determination of the "stress-deformation" behavior for MD systems. When compared with the Parrinello-Rahman method, the proposed approach clearly delineates under what conditions the Parrinello-Rahman scheme is valid.

Original languageEnglish (US)
Pages (from-to)6409-6432
Number of pages24
JournalInternational Journal of Solids and Structures
Issue number24-25
StatePublished - Dec 2005

All Science Journal Classification (ASJC) codes

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


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