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Advances in Mathematical Physics
Volume 2017 (2017), Article ID 4780928, 11 pages
Research Article

Contrast Expansion Method for Elastic Incompressible Fibrous Composites

1Department of Differential Equations and Statistics, Faculty of Mathematics and Natural Sciences, University of Rzeszow, Pigonia 1, 35-959 Rzeszow, Poland
2Pedagogical University, Ul. Podchorazych 2, 30-084 Krakow, Poland

Correspondence should be addressed to Vladimir Mityushev

Received 31 May 2017; Accepted 14 September 2017; Published 17 October 2017

Academic Editor: Andrei D. Mironov

Copyright © 2017 Piotr Drygaś and Vladimir Mityushev. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Contrast parameter expansion of the elastic fields for 2D composites is developed by Schwarz’s method and by the method of functional equations for the case of circular inclusions. A computationally efficient algorithm is described and implemented in symbolic form to compute the local fields in 2D elastic composites and the effective shear modulus for macroscopically isotropic composites. The obtained new analytical formula contains high-order terms in the contrast parameter and explicitly demonstrates dependence on the location of inclusions. As a numerical example, the hexagonal array is considered.