ISSN 打印: 1543-1649
ISSN 在线: 1940-4352

# 国际多尺度计算工程期刊

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

### ABSTRACT

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.

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