Contrast Expansion Method for Elastic Incompressible Fibrous Composites

Contrast Expansion Method for Elastic Incompressible Fibrous Composites

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 e...

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Bibliographic Details
Published in:Advances in mathematical physics Vol. 2017; no. 2017; pp. 1 - 11
Main Authors: Drygaś, Piotr, Mityushev, Vladimir
Format: Journal Article
Language:English
Published: Cairo, Egypt Hindawi Publishing Corporation 01-01-2017
Hindawi
Hindawi Limited
Subjects:
Applied mathematics
Archives & records
Boundary value problems
Composite materials
Computational fluid dynamics
Fiber composites
Functional equations
Inclusions
Integral equations
Materials science
Mechanics
Methods
Modulus of elasticity
Numerical analysis
Physics
Shear modulus
Two dimensional composites
Poland
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Summary: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.
ISSN:1687-9120
1687-9139
DOI:10.1155/2017/4780928