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International Journal for Multiscale Computational Engineering

 

ISSN for PRINT: 1543-1649

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$747.00

Issues per year:

6

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2003, Volume1

Issue 1

  134 pages  

DOI: 10.1615/IntJMultCompEng.v1.i1   

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  • Constitutive Modeling Based on Atomistics
  • Jacob Fish
    Multiscale Science and Engineering Center, Rensselaer Polytechnic Institute, Troy, NY 12189, USA

    Cyrille Schwob
    Departments of Civil, Mechanical, and Aerospace Engineering, Rensselaer Polytechnic Institute, Troy, NY 12180


    ABSTRACT

    Mathematical homogenization theory, which serves as a foundation for bridging multiple spatial and temporal scales for continuum systems, is generalized to provide a unified mathematical framework for bridging not only multiple continuum scales in space and time, but also multiple continuum and discrete scales. In this article, we study the one-dimensional chain of atoms and BCC crystals. The solution of the one-dimensional model problem is found to be in good agreement with the molecular dynamics simulation of the chain of atoms, whereas the classic approach based on the Cauchy–Born hypothesis is shown to produce significant errors.

    DOI: 10.1615/IntJMultCompEng.v1.i1.50

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