In this thesis we are interested in the propagation of low-frequency linear elastic waves through composite materials. We use a variety of dynamic homogenization techniques to find the effective elastic properties of some composites. We consider composites with isotropic phases for ease of exposition but the theory could easily be extended to anisotropic inclusions or host.We use a Representative Volume Element approach with the Method of Asymptotic Homogenization to model a random fibre-reinforced composite. The fibres are all aligned in the same direction and are taken to be of infinite extent, so the composite is essentially two-dimensional. For a random composite we have considered the anti-plane case for SH wave propagation and the in-plane case for P and SV elastic wave propagation, extending the previous published work of Parnell and Abrahams (2006), (2008a), in which a periodic fibre-reinforced composite was studied. We also show, for a simple example, that it is possible to extend the Representative Volume Element method to a three-dimensional particulate composite.In this thesis an Integral Equation Method for homogenization is also studied, with application to periodic fibre-reinforced composites. We have extended the work of Parnell and Abrahams (2008b), which considered SH wave propagation only, to the case of P and SV wave propagation.
| Identifer | oai:union.ndltd.org:bl.uk/oai:ethos.bl.uk:568644 |
| Date | January 2013 |
| Creators | Willoughby, Natasha |
| Contributors | Abrahams, David; Parnell, William |
| Publisher | University of Manchester |
| Source Sets | Ethos UK |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
| Source | https://www.research.manchester.ac.uk/portal/en/theses/dynamic-homogenization-for-the-elastic-properties-of-periodic-and-random-composites(da82e607-bc1f-40e9-8e62-ec5fbca1f68f).html |
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