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A Multi-Scale Computational Method Integrating Finite Element Method with Atomic Interactions of Materials

Bin Gu1,2,3, L. C. Zhang2, Weifeng Yuan1, Youjun Ning1

School of Manufacturing Science and Engineering, Southwest University of Science and Technology, Sichuan 621010, China
School of Mechanical and Manufacturing Engineering, The University of New South Wales, NSW2052, Australia
Corresponding author: Prof. Bin Gu. Tel: +86-816-6089898, Email:

Computer Modeling in Engineering & Sciences 2012, 88(4), 309-324.


Bridging the atomic and continuous analyses is an important aspect in multi-scale mechanics. This paper develops a computational method to integrate the atomic potential of a material with the finite element method. The novelty of this method is that strain energy is calculated from the atomic potential without the assumption in the Cauchy-Born rule that deformation in a virtual atomic cell is homogeneous. In this new method, the virtual atomic cell deformation is interpolated according to the continuum displacements associated with the shape functions. The applications of the method to single crystal Si and Ge bars under uniaxial tension and compression show that with a proper construction of the virtual atomic cell, the Young's modulii in the < 100 > , < 110 > and < 111 > directions obtained are in good agreement with the experimental measurements and MD simulations in the literature. Moreover, the simulated material's response to tension and compression is consistent with the interatomic interactions.


Cite This Article

Gu, B., Zhang, L. C., Yuan, W., Ning, Y. (2012). A Multi-Scale Computational Method Integrating Finite Element Method with Atomic Interactions of Materials. CMES-Computer Modeling in Engineering & Sciences, 88(4), 309–324.

This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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