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International Journal for Multiscale Computational Engineering
Facteur d'impact: 1.016 Facteur d'impact sur 5 ans: 1.194 SJR: 0.554 SNIP: 0.68 CiteScore™: 1.18

ISSN Imprimer: 1543-1649
ISSN En ligne: 1940-4352

International Journal for Multiscale Computational Engineering

DOI: 10.1615/IntJMultCompEng.2014007103
pages 33-43

BOUNDARY ELEMENT METHOD MODELLING OF NANOCOMPOSITES

Jacek Ptaszny
Institute of Computational Mechanics and Engineering, Silesian University of Technology, Konarskiego 18A, 44-100 Gliwice, Poland
Grzegorz Dziatkiewicz
Institute of Computational Mechanics and Engineering, Silesian University of Technology, Konarskiego 18A, 44-100 Gliwice, Poland
Piotr Fedelinski
Institute of Computational Mechanics and Engineering, Silesian University of Technology, Konarskiego 18A, 44-100 Gliwice, Poland

RÉSUMÉ

The paper deals with the numerical homogenization of polymer/clay nanocomposites reinforced by stacks of parallel clay sheets. The stacks can be modelled as effective particles, as it was shown in the literature. For a relatively small volume fraction of the reinforcement, the effective particles can be isotropic, while for greater values, the particles should be anisotropic. Other authors most commonly use analytical methods or the finite element method (FEM). In this work, the boundary element method (BEM) is applied. Two-dimensional plain strain models are analyzed. Two cases are considered, namely, isotropic and anisotropic (orthotropic) particles. The matrix of the composite is modelled as isotropic. The problem is solved by using a BEM formulation for plates containing many identical inclusions. The kernels of boundary integrals for the isotropic subdomains are the Kelvin solutions for plane elasticity. In the case of the orthotropic particles, fundamental solutions obtained by the Stroh formalism are applied. The results are compared to the Mori-Tanaka model. Acceptable agreement between the models is observed.

RÉFÉRENCES

  1. Beer, G., Smith, I., and Duenser, C., The Boundary Element Method with Programming for Engineers and Scientists.

  2. Brebbia, C. A. and Dominguez, J., Boundary Elements, An Introductory Course.

  3. Fedeliński, P., Ed., Advanced Computer Modelling in Micromechanics.

  4. Figiel, Ł. and Buckley, C. P., Elastic constants for an intercalated layered–silicate/polymer nanocomposite using the effective particle concept—A parametric study using numerical and analytical continuum approaches. DOI: 10.1016/j.commatsci.2008.09.005

  5. Hbaieb, K., Wang, Q. X., Chia, Y. H. J., and Cotterell, B., Modelling stiffness of polymer/clay nanocomposites. DOI: 10.1016/j.polymer.2006.11.062

  6. Kouznetsova, V., Brekelmans, W. A. M., and Baaijens, F. P. T., An approach to micro–macro modeling of heterogeneous materials. DOI: 10.1007/s004660000212

  7. Mura, T., Micromechanics of Defects in Solids.

  8. Nemat-Nasser, S. and Hori, M., Micromechanics: Overall Properties of Heterogeneous Materials.

  9. Pan, E., A BEM analysis of fracture mechanics in 2D anisotropic piezoelectric solids. DOI: 10.1016/S0955-7997(98)00062-9

  10. Ptaszny, J. and Fedeliński, P., Numerical homogenization of polymer/clay nanocomposites by the boundary element method.

  11. Sfantos, G. K. and Aliabadi, M. H., A boundary cohesive grain element formulation for modelling intergranular microfracture in polycrystalline brittle materials. DOI: 10.1002/nme.1831

  12. Sheng, N., Boyce, M. C., Parks, D. M., Rutledge, G. C., Abes, J. I., and Cohen, R. E., Multiscale micromechanical modeling of polymer/clay nanocomposites and the effective clay particle. DOI: 10.1016/j.polymer.2003.10.100

  13. Ting, T. C. T., Anisotropic Elasticity, Theory, and Applications.

  14. Wang, J. and Pyrz, R., Prediction of the overall moduli of layered silicate-reinforced nanocomposites, Part I. Basic theory and formulas. DOI: 10.1016/S0266-3538(03)00024-1

  15. Wang, J. and Pyrz, R., Prediction of the overall moduli of layered silicate-reinforced nanocomposites, Part II. Analyses. DOI: 10.1016/S0266-3538(03)00025-3

  16. Wang, Y. M. and Ting, T. C. T., The Stroh formalism for anisotropic materials that possess an almost extraordinary degenerate matrix N. DOI: 10.1016/S0020-7683(96)00024-8

  17. Yao, Z., Kong, F., and Zheng, X., Simulation of 2D elastic bodies with randomly distributed circular inclusions using the BEM.

  18. Zohdi, T. I. and Wriggers, P., An Introduction to Computational Micromechanics.


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