Research into mathematical approaches to the modelling and study of continuous media.
Research into mathematical approaches to the modelling and study of continuous media. Contemporary research in continuum mechanics is erasing the traditional distinction between solid and fluid mechanics, and includes mathematical approaches to understanding materials that can exhibit fluid and solid behaviour, as well electromagnetic, biochemical or multiphysical continua.
This research area also addresses the interaction and interfaces between distinct media (for example, in the behaviour of suspensions and granular material, flow in porous media, composites and advanced materials), and may incorporate aspects of complexity science. Applications of this research include those in the biological and life sciences. Research specifically focused on continuum modelling of biological matter is not included in this area, but is considered under the Mathematical biology research area.
Contemporary developments in this field have led to a broad range of new applications arising from increasing emphasis on developing mathematical descriptions of complex media – for example, photonic crystals, granular materials, dense suspensions, polymers, composites and metamaterials. Understanding such media is of substantial importance in a range of sectors, and will provide fundamental insights to underpin delivery of EPSRC prosperity outcomes.
The emergence of such novel applications, combined with the UK’s legacy of internationally excellent research in continuum mechanics, offers the opportunity for the UK to establish itself at the forefront of fundamental research in complex media and related applications.
We aim to:
- develop a strengthened portfolio of high-quality research and skills in multiphysical modelling of a variety of complex media encompassing solid and fluid mechanics, to support emerging scientific challenges in fluid dynamics and aerodynamics, complex fluids and rheology, biophysics and soft matter physics, particle technology and advanced materials, as well as photonic materials and metamaterials
- grow the solid mechanics portfolio of high-quality research and skills which complement the advanced materials strategy
- maintain a world-leading portfolio of research and skills in theoretical fluid mechanics
- enhance intradisciplinary links within continuum mechanics and between continuum mechanics and other areas of mathematical sciences – for example, mathematical biology, mathematical analysis, numerical analysis, nonlinear systems, and statistics and applied probability
- encourage greater integration between theoretical, numerical and experimental research – for example by building on links developed by the UK Fluids Network and encouraging coordination of access to existing equipment and requirements for new equipment
- develop further connections with industrial and other users of continuum mechanics research, building on UK excellence in industrial mathematics.
To help us realise these goals, researchers are encouraged to:
- take advantage of mathematical sciences infrastructure to develop connections across the mathematical sciences, with other disciplines and with industry
- engage with existing relevant investments, such as the UK Fluids Network, the High Value Manufacturing Catapult and the Henry Royce Institute for advanced materials
- take inspiration from the EPSRC prosperity outcomes, especially relating to productive and resilient nation, and the Global Challenges Research Fund
- maximise use of existing facilities and equipment, and coordinate requirements for new equipment, where possible.