Modelling of the mechanisms governing crimp in wool

This thesis considers modelling one of the mechanisms, which governs the formation of wool fibres. The problem is investigated by constructing a mathematical model that is based on the geometry of the ultrastructure of the wool fibres. The deformed shapes of the wool fibres are obtained by minimising the strain energy calculated from the mathematical model. The objective of this study is to explore the relationship between the ultrastructure and the crimpy shape of the wool fibres. The first chapter gives the background information of wool fibre, the outline of the thesis and defines the problem. The second chapter examines the structures inside the wool fibres and the mechanisms, which govern the shapes of the wools fibres. The variables used to describe the fibre shapes are introduced here. Then, some simple examples are given to demonstrate the mathematical model. In the third chapter, the structures of the wool fibres are simplified with several assumptions and used to construct the basic model. Then, some results are given with various values of different parameters to demonstrate the properties of the model. Some modifications of the model are made, which include the addition of the cuticle shell and an approximate analytical model by Taylor's expansion. The fourth chapter develops another modification of the mathematical model with the addition of a 'macrofibril' structure. The fifth chapter gives the last modification of the model uses integration to calculate the total energy of the whole fibre. The sixth and the seventh chapters show the practical methods to measure the natural shape of a single fibre and the cross-section pattern of the fibre respectively. The measured natural shape of the wool fibre can be used to verify the local estimated shape of the wool fibre, which is calculated by the mathematical model with the measured cross-section pattern