Homogenization Methods to Approximate the Effective Response of Random Fibre-reinforced Composites

Willoughby, Natasha and Parnell, William J. and Hazel, Andrew L. and Abrahams, I David (2011) Homogenization Methods to Approximate the Effective Response of Random Fibre-reinforced Composites. International Journal of Solids and Structures. (In Press)

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Abstract

In this article a fibre-reinforced composite material is modelled via an approach employing a Representative Volume Element with periodic boundary conditions. The effective elastic moduli of the material are thus derived. In particular, the method of asymptotic homogenization is used where a finite number of fibres are randomly distributed within the representative periodic cell. The study focuses on the efficacy of such an approach in representing a macroscopically random (hence transversely isotropic) material. Of particular importance is the sensitivity of the method to cell shape, and how this choice affects the resulting (configurationally averaged) elastic moduli. The averaging method is shown to yield results that lie within the Hashin-Shtrikman variational bounds for fibre-reinforced media and compares well with the multiple scattering and (classical) self-consistent approximations with a deviation from the latter in the larger volume fraction cases. Results also compare favourably with well-known experimental data from the literature.

Item Type: Article
Uncontrolled Keywords: Asymptotic homogenization, fibre-reinforced composites, microstructure, representative volume element, effective properties, anisotropy
Subjects: MSC 2010, the AMS's Mathematics Subject Classification > 74 Mechanics of deformable solids
PACS 2010, the AIP's Physics and Astronomy Classification Scheme > 40 ELECTROMAGNETISM, OPTICS, ACOUSTICS, HEAT TRANSFER, CLASSICAL MECHANICS, AND FLUID MECHANICS > 46 Continuum mechanics of solids
Depositing User: Dr William J Parnell
Date Deposited: 06 Mar 2012
Last Modified: 20 Oct 2017 14:13
URI: http://eprints.maths.manchester.ac.uk/id/eprint/1788

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