Analytical Studies on Phase Transitions in Homogeneous and Inhomogeneous Cylinders Composed of Compressible Elastic Materials
DescriptionPhase-transforming materials such as shape memory alloys (SMAs) and shape memory polymers have broad applications. Mathematical analysis and modelling for the behaviour of this type of materials is essential for application purposes. This project will study the problems of phase transitions in homogeneous and inhomogeneous slender cylinders composed of compressible elastic materials with non-convex energy functions. The researchers will present reasons, both experimental and mathematical, why it is important to consider the radial deformation for phase transitions in slender elastic cylinders. When the radius of the cylinder is much smaller than its length, it is possible to use an asymptotic approach to capture such influences. It is expected that the derived model equations can capture all the essential physical effects and are still analytically treatable. Both qualitative and quantitative analysis for the solutions will be conducted. In particular, the research will examine the possibility of whether due to the inhomogeneity of the radius a configuration with multiple phase transformation fronts can arise. The analytical results are expected to help understand the main features of phase transformations in slender structures.
|Effective start/end date||1/12/07 → 19/08/11|