Area of investment and support

Area of investment and support: Continuum mechanics

Research into mathematical approaches to the modelling and study of continuous media.

Partners involved:
Engineering and Physical Sciences Research Council (EPSRC)

The scope and what we're doing

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 multi-physical 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 multi-physical 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 co-ordination 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.

Why we're doing it

The UK is world-leading in fluid mechanics and, in recent years, the quality of UK research has been recognised through the award of international prizes to researchers from this country. In addition, the UK has a high-quality research community in solid mechanics which, although smaller by international comparison, is well-positioned to develop and contribute effectively to key outcomes – for example, through complementing with the advanced materials strategy.

The importance of continuum mechanics is underlined by the UK’s strong tradition of industrial mathematics, which includes a core of research in areas such as combustion, process modelling, solidification, complex fluids in porous media, and composite modelling. While industry or Innovate UK funds much of this, there is a need for underpinning research and training if the UK is to maintain its leading position.

UK innovations in mathematical knowledge exchange, particularly from continuum mechanics to end-users, have been exported to the rest of the world and have helped establish the UK as a centre of user-inspired mathematical research.

Evidence from the Research Excellence Framework (REF) 2014 exercise indicates that overall researcher numbers in continuum mechanics have been maintained. There is considerable provision for training in fluid mechanics, with several EPSRC-supported centres for doctoral training (CDTs) having at least some projection into the area. However, the UK does not have the same level of capacity as its international competitors in important sub-disciplines – for example, multiphysics modelling and solid mechanics – and is at risk of falling behind in key emerging areas.

Past projects, outcomes and impact

Visualising our portfolio (VoP) is a tool for users to visually interact with the EPSRC portfolio and data relationships. Find out more about research area connections and funding for continuum mechanics.

Find previously funded projects on Grants on the Web.

Who to contact

Rachael Pittaway, Portfolio Manager, Mathematical Sciences

Email: rachael.pittaway@epsrc.ukri.org

Telephone: 07874 884070

Alternatively, contact: maths@epsrc.ukri.org

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