Strategic Support Package: Engineering of Active Materials by Multiscale/Multiphysics Computational Mechanics

Continuum Mechanics describes the response of solid and fluid systems subject to loading. The primary assumption of Continuum Mechanics is that matter can be viewed as a continuous distribution. This view of the world is termed macroscopic and has served the engineering community well, allowing for the virtual design of complex structures. In recent years, however, the engineering of structures at the microscopic scale has become ubiquitous. Applications include computer processors, medical devices, cellular technology, among others.

As the size of components and devices decrease to the microscopic scale and beyond, so the classical continuum assumptions become less valid. That is, the discrete nature of matter starts to play a role giving rise to size effects. Classical continuum formulations do not possess a length scale and are unable to predict size effects. Thus, computer models based on these continuum formulations (typically finite element models) are of limited engineering value.

Active materials - materials that change their structure when subjected to a non-mechanical field - have numerous applications in engineering, for examples, as artificial muscles or as actuators. The interaction between the material and the applied fields gives rise to a coupled problem. The research proposed here will develop formulations for coupled problems to enable the next generation of active materials with optimised macrostructural and microstructural form tailored to function. The fields to couple with the mechanical one include thermal, electric, magnetic, and chemical.

To optimise the microscopic structure of a material one must have a robust and accurate continuum model that captures size effects. Linking the macroscopic and microscopic scales will be accomplished using a new class of micro-to-macro transition techniques for coupled problems - also termed computational homogenisation. The fundamental idea is to transfer information concerning the loading from the macroscopic scale down, and then to solve a problem at the microscopic scale that captures all the key features that give rise to coupling and size effects. The averaged (homogenised) response is then returned to the macroscopic scale. Following this approach, crude assumptions regarding the microscopic structure can be avoided leaded to more accurate and predictive simulations. The coupling of multiple fields across the scales is however very challenging and requires the development of new algorithms and continuum formulations.

Optimisation theory allows one to design a component to maximise a certain function of interest subject to various constraints. The theory is relatively mature for engineered products at the macroscopic scale. This is not the case at the microscopic scale and certainly not the case for multiscale product design.

The ability to optimally design and engineer active materials from the microscopic scale up will lead to a step-change in product functionality and design. The objective of the research is the enable this revolution through advanced algorithms and computational models.

In addition to the stated scientific objectives, the research will underpin the formation of a new Centre of Excellence in Computational Engineering & Discovery. The Centre aims to promote mechanics in the UK by taking a leading role in the organisation of workshops and seminars, and through the education and development of postgraduate researchers.

The impact of the Centre on Computational Mechanics and related disciplines in the UK and beyond will be significant. This strategic support package reflects the need to reinvigorate computational mechanics research in the UK and to bolster academic leadership.

The research undertaken at the Centre and enabled by the support package will contribute significantly to and extend the body of knowledge on active materials. The impact of the scientific research will be ensured by publishing the findings in high-quality journals such as Mathematics and Mechanics of Solids, Computational Material Science, International Journal of Solids and Structures, Computer Methods in Applied Mechanics and Engineering, and the Journal of Mechanics and Physics of Solids. Steinmann has published extensively in these journals.

The work will be presented at multiple international conferences. Steinmann is regularly invited as a presenter at such events. This will ensure that the research has considerable impact. Steinmann will organise a mini-symposium at ECCM-ECFD (Glasgow 2018) and propose an ECCOMAS thematic conference (Glasgow 2019) on "Optimisation across the scales". In addition, he will propose a summer school course at the International Centre for Mechanical Sciences (CISM) on a similar topic. Steinman has a proven track record of organising both thematic conferences and CISM courses.

Regular colloquia will be held at the UoG to communicate our findings to the Computational Mechanics community and industry at large. The Centre will actively engage with industry to ensure that they are aware of the significant impact that active materials and our research will have.

The impact of a considerable amount of current research in Computational Mechanics is limited by the closed nature of the software developed to realise the mathematical models. It takes considerable time and financial resources to simply reproduce supposed benchmark problems in the literature. This presents a significant obstacle to emerging researchers and is contrary to the spirit of scientific discovery. The Centre will ensure that all code developed is made open-source and is based upon high-quality numerical libraries such as deal.II. Steinmann and his current group are active developers and contributors to the open-source deal.II community. These efforts have the impact of initiating international collaborations and enabling others to do research.

In addition to written publications, the research will be made accessible and available to industry and the public through a range of engagement activities. The colloquia, described above, will be used to develop a wider stakeholder base, supported by the Business Development Manager provided by the UoG, informing and engaging potential collaborators of the Centre and its research. Thus, industry will be made aware of research findings and will have ample opportunity to provide timely feedback. Societal impact will be through the design and optimisation of smart devices using active materials, with applications ranging from energy conversion and harvesting, to healthcare technologies.

Computer-aided virtual prototyping through the design and optimisation of active materials for smart devices is an ideal vehicle for engaging the broader public and fostering an interest in science and technology. Therefore, the research and the Centre will be used to popularise engineering and science particularly among school children. The research will be presented at the annual Glasgow Science Festival. A blog site and Twitter feed detailing the Centre's activities will be launched at the beginning of the project. Publications and workshop proceedings will be covered by the media and press releases will be issued accordingly.