International Journal for Multiscale Computational Engineering

ISSN for PRINT: 1543-1649

For Online Access

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2003, Volume1

Issue 1

134 pages

DOI: 10.1615/IntJMultCompEng.v1.i1

Issue price - $178.00

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

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 Download article, 14 pages

Article price - $35.00

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