A general continuum theory of polycrystalline materials
Lead Research Organisation:
University of Leeds
Department Name: Applied Mathematics
Abstract
Materials such as ice, rock salts and the Earth's mantle flow as highly viscous fluids over a long time. For example, the flow of a glacier is similar to the spread of golden syrup over a kitchen table. However, due to the crystal structure of ice and rock at small scales, they flow in interesting and unusual ways compared to normal fluids. Such flows are called polycrystalline. These flows are of critical importance: the flow of ice is the main contributor to sea-level rise and understanding the flow of the Earth's mantle is central to plate tectonics. Understanding the flow of salt in caverns is also important as there is an increasing need to use these caverns to store hydrogen as part of the net zero energy transition.
Polycrystalline flows form a crystal structure on a small scale, which allows them to flow faster in certain directions, depending on the orientation of the crystals. Therefore, understanding and predicting how the crystal structure evolves is key for predicting these flows at a large scale. This proposal addresses this challenge by developing a new approach of formulating equations and computer models that can predict the microstructure of any polycrystalline material. The key development is to model the crystal structure using a statistical field that averages over many crystal grains, rather than modelling grains directly. This "continuum" approach is analogous to how flow of fluids like water and air can be modelled by average quantities like velocity and density, rather than by looking at individual molecules. The approach reduces the model to relatively few empirical parameters, which can be systematically calibrated using experimental data. By circumventing the need to resolve each grain of the crystal structure within the model, the continuum approach confers substantial gains in terms of accuracy and predictive capability, opening news doors to efficient and highly resolved simulations of polycrystalline flows.
Long-term, the results will support improved predictions for future sea-level rise due to ice-sheet flow, better understanding of the Earth's mantle and plate tectonics, and better understanding of the flow of other materials, such as rock salts in caverns - helping with the transition to net zero.
Polycrystalline flows form a crystal structure on a small scale, which allows them to flow faster in certain directions, depending on the orientation of the crystals. Therefore, understanding and predicting how the crystal structure evolves is key for predicting these flows at a large scale. This proposal addresses this challenge by developing a new approach of formulating equations and computer models that can predict the microstructure of any polycrystalline material. The key development is to model the crystal structure using a statistical field that averages over many crystal grains, rather than modelling grains directly. This "continuum" approach is analogous to how flow of fluids like water and air can be modelled by average quantities like velocity and density, rather than by looking at individual molecules. The approach reduces the model to relatively few empirical parameters, which can be systematically calibrated using experimental data. By circumventing the need to resolve each grain of the crystal structure within the model, the continuum approach confers substantial gains in terms of accuracy and predictive capability, opening news doors to efficient and highly resolved simulations of polycrystalline flows.
Long-term, the results will support improved predictions for future sea-level rise due to ice-sheet flow, better understanding of the Earth's mantle and plate tectonics, and better understanding of the flow of other materials, such as rock salts in caverns - helping with the transition to net zero.
