Continuum mechanics

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 (e.g. 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 (e.g. 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.

By the end of the Delivery Plan, we aim to have:

  • Developed 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
  • Grown the solid mechanics portfolio of high-quality research and skills which complement the Advanced Materials Strategy
  • Maintained a world-leading portfolio of research and skills in theoretical fluid mechanics
  • Enhanced intradisciplinary links within Continuum Mechanics and between Continuum Mechanics and other areas of mathematical sciences (e.g. Mathematical Biology, Mathematical Analysis, Numerical Analysis, Non-Linear Systems, and Statistics and Applied Probability)
  • Encouraged greater integration between theoretical, numerical and experimental research (e.g. by building on links developed by the UK Fluids Network and encouraging co-ordination of access to existing equipment and requirements for new equipment)
  • Developed 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 Sir 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 co-ordinate requirements for new equipment, where possible

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 to contribute effectively to key Outcomes (e.g. through complementing with the Advanced Materials Strategy) (Evidence source 1,2,3).

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 source 4,5).

Evidence from the Research Excellence Framework (REF) 2014 exercise indicates that overall researcher numbers in Continuum Mechanics have been maintained over the last Delivery Plan period (Evidence source 6). 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 (e.g. multiphysics modelling and solid mechanics) and is at risk of falling behind in key emerging areas (Evidence source 1,2,3).

This area will contribute to the Resilient and Productive Nation Outcomes, and the following specific Ambitions:

P1: Introduce the next generation of innovative and disruptive technologies

Enabling design of advanced materials with bespoke properties, or combinations of properties, will in turn enable the introduction of new products.

P3: Establish a new place for industry that is built upon a 'make it local, make it bespoke' approach

Advanced understanding of the behaviour of complex fluids and materials will enable faster, efficient 3D printing and other fabrication technologies to enable manufacturing closer to the customer.

P5: Transform to a sustainable society, with a focus on the circular economy

This research area will model and design alternative materials which meet new requirements for safety, security of supply and environmental impact.

R1: Achieve energy security and efficiency

Providing mathematical tools to understand fluid mechanical processes is important in enabling secure, efficient energy generation technologies.

R5: Build new tools to adapt to and mitigate climate change

Improved understanding of atmospheric processes will help predict extreme weather events.

Research area connections

This diagram shows the top 10 connections between Research Areas within the EPSRC research portfolio. The depth of the segment relates to value of grants and the width of the segment relates to the number of grants shared by those two Research Areas. Please click to see the related Research Area rationale.

Visualising our Portfolio (VoP)
Visualising our portfolio (VoP) is a tool for users to visually interact with the EPSRC portfolio and data relationships.

EPSRC support by research area in Continuum mechanics (GoW)
Search EPSRC's research and training grants.

Contact Details

In the following table, contact information relevant to the page. The first column is for visual reference only. Data is in the right column.

Name: Michael Ward
Job title: Manager
Department: Mathematical Sciences
Organisation: EPSRC
Telephone: 01793 444196