Composite materials are ubiquitous in industry since they possess material properties which can be optimized for use in a specific context. Many offer a combination of properties which cannot be obtained with simple homogeneous media. They are particularly useful in the context of underwater acoustics, but their complexity makes mathematical modelling and prediction of effective properties a significant challenge.

The composite material of primary interest in the project is of a host/inclusion type, consisting of two distinct phases: small spherical shells distributed throughout a rubber host phase. The rubber nature of the host phase means that it deforms nonlinearly under pre-stress since the deformation is not only large but its constitutive behaviour is nonlinear. This pre-stress causes microstructure evolution and localized strained regions to develop throughout the composite.

This project aims to improve the understanding of the behaviour of random composites and/or pre-stressed composites capable of large deformation. Specifically the issue of low frequency excitation will be addressed. Numerical methods are costly in terms of computational time and resources, and do not give a great deal of insight into the physical processes involved. Therefore, mathematical homogenization schemes will be developed and extended in order to tackle the various model problems.

Project staff and support

Natasha Willoughby (Postgraduate Associate, University of Manchester)
David Abrahams (Academic supervisor, University of Manchester)
William Parnell (Academic supervisor, University of Manchester)
Peter Brazier-Smith (Industrial supervisor, Thales Underwater Systems)
David Allwright (Technology Translator, Industrial Mathematics KTN)

This project is being carried out at the University of Manchester, in conjunction with Thales Underwater Systems. It is supported by an EPSRC industrial CASE award, made available through the Knowledge Transfer Network for Industrial Mathematics. Start date: October 2006; duration: 3.5 years.