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International Journal for Multiscale Computational Engineering
Impact-faktor: 1.016 5-jähriger Impact-Faktor: 1.194 SJR: 0.554 SNIP: 0.68 CiteScore™: 1.18

ISSN Druckformat: 1543-1649
ISSN Online: 1940-4352

International Journal for Multiscale Computational Engineering

DOI: 10.1615/IntJMultCompEng.v1.i1.50
14 pages

Constitutive Modeling Based on Atomistics

Jacob Fish
Civil Engineering and Engineering Mechanics, Columbia University, New York, New York 10027, 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.