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The loss of ice from Antarctica and Greenland is the main source of uncertainty for sea-level rise predictions under a warming climate. Ice fabrics - the distribution of crystal orientations within a polycrystal - are key for understanding the dynamics of ice. Understanding ice fabrics enables us to infer processes occurring within ice sheets. In addition, ice fabrics can cause the flow rate to vary by a factor of 9 in different directions. Despite this, it is still a challenge to model ice fabrics both accurately and efficiently. I develop the first fully constrained continuum model for fabric evolution which agrees with experimental results and has only temperature and velocity gradient as inputs, with low computational cost. Using this model I explore fabrics generated across a spectrum of two-dimensional deformations and temperatures. Results show that intermediate deformation regimes between pure and simple shear result in a smooth transition between a fabric characterised by a cone-shape and a secondary cluster pattern. Highly-rotational deformation regimes produce a weak girdle fabric. I also predict fabrics within an ice stream and compare results to measured ice fabrics from cores at the East Greenland Ice Core Project (EGRIP) site by tracing the flow path upstream using satellite data. This approach correctly predicts the fabric pattern at EGRIP - a girdle/horizontal maxima perpendicular to the flow. The results also provide insights into properties deep within the ice sheet such as the level of basal slip. In summary, the fabric model and its applications presented in this thesis enable prediction of ice fabrics much more accurately and easily than previously. Due to its numerical efficiency the developed and tested fabric evolution model presented in this work can now be coupled to large-scale ice-sheet models and provide a reliable basis for estimating the effect of viscous anisotropy.

This thesis presents the development of sagittal based transducers for ultrasonically assisted large bone cutting. Bone cutting of large bones is a widely used methodology, typically carried out with the use of sagittal saws. Ultrasonic machining has shown benefits over unassisted conditions, with greater cut speeds and improved surface finishes. Ultrasonic bone cutting is carried out currently for small bone surgeries but shows similar benefits. In this thesis, the design and development of a series of transducers based upon sagittal blades, is detailed, including their design, manufacture, characterisation, and cut testing. An initial study was conducted with designs based upon commercial blades. Finite element analysis was used to optimise their design, and post manufacture, experimental modal analysis and impedance analysis were used to characterise the two transducers. Cut testing was conducted, with an improved cut time of 0.05 and 0.19 seconds, and a decrease in temperature of 2.1 and 4.8 °C for the two transducers compared to control conditions. Subsequently, a study was carried out to develop the epoxy layer used to adhere the piezoceramic of the planar transducer to the substrate. Three investigation parameters are defined; substrate machining technique, epoxy composition, and layer thickness. Twelve transducers were produced, and characterised again using impedance analysis, experimental modal analysis, and harmonic analysis. It was concluded that the most suitable epoxy conditions would be a milled machined substrate process along with a 50 μm epoxy layer, and a 2:1 epoxy composition. Using the established epoxy parameters, two surface and two embedded planar transducers, and one Langevin transducer were developed using finite element analysis. The transducers were manufactured, and characterised. The measured operational frequencies were 28.6 kHz, 26.6 kHz, 24.8 kHz, 30 kHz, and 22.5 kHz for the Langevin, short surface, long surface, short embedded, and long embedded transducer respectively. These transducers were then used for a series of cut tests. Firstly, several drag tests were conducted using a specifically designed rig. Investigation parameters included the current draw of the drive actuator, the cut depth, the cut medium, and the applied load. The key findings of the ultrasonic assisted cuts at a 16 N load and 4 μm desired displacement, were a 29% greater depth of cut than the control cuts. With a 16 N load and an 8 μm desired ultrasonic displacement, a 77% greater depth of cut was found compared to control conditions. At 8 N load, the Langevin transducer achieved a 233% and 166% greater depth of cut on average than the corresponding control condition with a 10 and 8 μm desired ultrasonic displacement. Subsequently, sagittal cutting using a sagittal handpiece was carried out within a designed rig. Cuts were conducted at varying handpiece speeds, with time to complete cut and peak temperature recorded. The results showed little distinction between ultrasonically assisted and control conditions, with a slight reduction of an average of 0.5 seconds for ultrasonically assisted cuts at 100% handpiece speed. Large differences in cut depth were found for ultrasonically assisted sagittal cutting at low speeds, supporting the hypothesis outlined at the start of this thesis. Higher speeds cuts showed little improvement, but further refinement could be carried out with future work.