Mathematical fundamentals of Metamaterials for multiscale Physics and Mechanics

Metamaterials are materials that are man-made and can have properties that no natural material could have, for instance light entering a metamaterial slab can be bent in the opposite manner to that which one would usually expect. This is not merely a scientific curiosity, it can have profound implications leading to sub-wavelength imaging, focusing, invisibility cloaks amongst other effects and this, in turn, can lead to materials with unexpected and novel properties. Much of the interest in metamaterials has thus far been in optics and electromagnetism, but it is clear that the underlying ideas should be applicable in other contexts such as elasticity, diffusion, structured materials, acoustics and even water waves. There is an abundance of important applications: designing thermal cloaks for keeping sensitive electronics cool, creating acoustic metamaterials for underwater stealth, wave by-pass systems for structural protection of buildings or key components, all of which are outside the optical context of metamaterials as they currently exist.
A key issue in creating a metamaterial is its design, normally as a periodic medium with a precise micro-structured geometry, and the frequency at which it operates.
As Metamaterials are beginning to achieve a certain maturity in optics the time is ripe to move this knowledge coherently into other fields, it is also timely to enrich Mathematics with the exciting conceptual problems created in Metamaterials and enrich the Metamaterials toolkit with sophisticated Mathematical techniques. This proposal aims to use the transformative tools and unifying ideas of Mathematics to move the physics of Metamaterials into research areas such as Elasticity, Acoustics, Structural Mechanics and Diffusion where Metamaterials have barely been investigated, but where there will undoubtedly be impact and applications. By working closely with Physicists it will enrich and empower the existing Metamaterials community by bringing sophisticated numerical and theoretical methods to the fore.

The potential impact of Metamaterials outside Optics is very broad, for instance in cloaking buildings from ground vibration: Menard (a French Civil Engineering company) is constructing trial sites using ideas (based upon work by our visiting Fellow, Guenneau, that draws upon his joint work with two of the proposers) and this UK Mathematics-led science is currently leading to French Engineering impact. All three groupings have a strong track-record of impact. As an exemplar: Craster has had a decade-long collaboration with the RCNDE at Imperial which has led to algorithms being incorporated into DISPERSE (the world's-leading software modelling tool for guided stress waves, licensed by Imperial Consultants) and by Rolls-Royce amongst others and a similar relationship with MoD DSTL.

Our approach to impact will be pro-active: We have deliberately incorporated an industry transfer Fellow into our research team, Professor Ian Jones from Liverpool John Moores University; he is the Director of the Mechanical Engineering and Materials Research Centre and brings invaluable modelling experience from his time in industry with links that he has maintained in academia through contract research and consultancy assignments with UKAEA, AEA Technology, Serco Assurance and AMEC. We will develop these existing strategic partnerships in NDE, using the links of Jones, with the nuclear industry (Rolls Royce and AMEC) where elastic multi-scale media is a key issue. Other members of the research team have contacts with MoD DSTL, BAE Systems, Rolls-Royce and utilising the well established Imperial College Industry Clubs, focused industry workshops will be run. A dedicated website will be created and we will actively engage in EngD and CASE doctorate programmes. Importantly both BAE Systems and MoD DSTL have expressed strong interest in playing an active role in this grant by sitting on the advisory board; MoD DSTL have offered additional support through a funded PhD studentship.

Additionally, research findings will be disseminated widely through journal publications, national and international conference talks, a dedicated website, public engagements and through the focused workshops that we propose to run. The development of strategic international partnerships is also a key element of our approach to impact, we will develop and leverage the existing strong links with the CNRS and CUDOS by funded joint Phd positions (using Phd students leveraged from our institutions) and through visitor exchanges. We will be active in public engagement and outreach activities, the subject of Metamaterials is fascinating and appealing outside academia, and a program of external public lectures, school visits etc will be incorporated into the work programme.