Roadmap on metamaterial theory, modelling and design

Davies, Bryn ORCID: https://orcid.org/0000-0001-8108-2316, Szyniszewski, Stefan ORCID: https://orcid.org/0000-0002-7862-8506, Dias, Marcelo A ORCID: https://orcid.org/0000-0002-1668-0501, de Waal, Leo ORCID: https://orcid.org/0000-0003-0487-3848, Kisil, Anastasia, P Smyshlyaev, Valery ORCID: https://orcid.org/0000-0002-5209-2272, Cooper, Shane, Kamotski, Ilia V, Touboul, Marie ORCID: https://orcid.org/0000-0003-4052-0994, Craster, Richard V ORCID: https://orcid.org/0000-0001-9799-9639, Capers, James R, Horsley, Simon A R, Hewson, Robert W, Santer, Matthew, Murphy, Ryan, Thillaithevan, Dilaksan, Berry, Simon J, Conduit, Gareth J, Earnshaw, Jacob, Syrotiuk, Nicholas, Duncan, Oliver ORCID: https://orcid.org/0000-0001-9503-1464, Kaczmarczyk, Łukasz, Scarpa, Fabrizio ORCID: https://orcid.org/0000-0002-5470-4834, Pendry, John B, Martí-Sabaté, Marc ORCID: https://orcid.org/0000-0001-7646-0546, Guenneau, Sébastien, Torrent, Daniel, Cherkaev, Elena, Wellander, Niklas, Alù, Andrea ORCID: https://orcid.org/0000-0002-4297-5274, Madine, Katie H ORCID: https://orcid.org/0000-0001-6135-5495, Colquitt, Daniel J ORCID: https://orcid.org/0000-0001-5637-1626, Sheng, Ping, Bennetts, Luke G ORCID: https://orcid.org/0000-0001-9386-7882, Krushynska, Anastasiia O ORCID: https://orcid.org/0000-0003-3259-2592, Zhang, Zhaohang ORCID: https://orcid.org/0000-0003-4215-6604, Mirzaali, Mohammad J and Zadpoor, Amir (2025) Roadmap on metamaterial theory, modelling and design. Journal of Physics D: Applied Physics, 58 (20). ISSN 1361-6463

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Abstract

This Roadmap surveys the diversity of different approaches for characterising, modelling and designing metamaterials. It contains articles covering the wide range of physical settings in which metamaterials have been realised, from acoustics and electromagnetics to water waves and mechanical systems. In doing so, we highlight synergies between the many different physical domains and identify commonality between the main challenges. The articles also survey a variety of different strategies and philosophies, from analytic methods such as classical homogenisation to numerical optimisation and data-driven approaches. We highlight how the challenging and many-degree-of-freedom nature of metamaterial design problems call for techniques to be used in partnership, such that physical modelling and intuition can be combined with the computational might of modern optimisation and machine learning to facilitate future breakthroughs in the field.