My thesis title: Homogenization techniques for wave propagation in composite materials
What does this mean?
- Composite material. A composite material is a material that is produced from two or more constituents, which usually have quite distinct properties. This usually gives rise to a material that has enhanced properties, e.g. unusually stiff or conductive. Composites typically have a microstructure which can be as small as hundreds of nanometres.
- Wave propagation. By “waves” here we mean any wave that propagates through a composite material, so it could be an acoustic, elastic or electromagnetic wave. Although the physics of these waves are quite different, the mathematics governing how we describe them is remarkably similar and so it means that methods developed for one type of wave can be used to describe another type with remarkable ease.
- Homogenization technique. Mathematically, homogenization is the study of differential equations with rapidly oscillating coefficients. This is important because given that composites consist of at least two different constituents, the properties of the material change with space and often over a very small length scale as noted above. Mathematically, this manifests itself as a differential equation that governs some physical property (e.g. acoustic pressure) with coefficients that vary rapidly in space, corresponding to e.g. density or bulk modulus.
The homogenisation technique makes sense of what the waves “see” or “feel” when they propagate through the composite material in question, normally working best in the case when the wave’s wavelength is much longer than the variation in microstructure. The techniques allow one to determine the “effective material properties” of the composite medium. I focussed mainly on elastic properties in my PhD.
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