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

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

Research output: Contribution to journalArticle

12 Citations (Scopus)

Abstract

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
Volume42
Issue number24-25
DOIs
StatePublished - Dec 1 2005

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homogenizing
Homogenization
Molecular Dynamics Simulation
Molecular dynamics
Continuum
molecular dynamics
continuums
Molecular Dynamics
Computer simulation
Heterogeneous Media
simulation
Constitutive Relations
Particle System
Large Deformation
Discrete Systems
Dynamic Systems
Valid
Dynamical systems
Model

All Science Journal Classification (ASJC) codes

  • Modeling and Simulation
  • Materials Science(all)
  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering
  • Applied Mathematics

Cite this

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A Lagrangian-based continuum homogenization approach applicable to molecular dynamics simulations. / Andia, P. C.; Costanzo, F.; Gray, G. L.

In: International Journal of Solids and Structures, Vol. 42, No. 24-25, 01.12.2005, p. 6409-6432.

Research output: Contribution to journalArticle

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AU - Costanzo, F.

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