Micromorphic models and effective interface forces for finite-sized mechanical metamaterials modeling

Prof. Dr. Angela Madeo, Technische Universität Dortmund

Metamaterials are architectured materials whose mechanical properties go beyond those of classical materials, thanks to their heterogeneous microstructure. This allows them
to show exceptional static/dynamic features such as negative Poisson’s ratio, twist in response to being pushed or pulled, band-gaps, cloaking, focusing, channeling, negative refraction, etc.

In the last two centuries, the advancement of knowledge on finite-size classical-materials modeling has enabled the design of engineering structures (buildings, bridges, airplanes, cars, etc.) resisting to static and dynamic loads.

Today, while the modeling of infinite-size metamaterials is achievable via reliable homogenization techniques, we must acknowledge that these techniques are intrinsically unsuitable for finite-size metamaterials’ modeling. This conceptual gap prevents us to explore finite-sized metamaterials/classical-materials structures and optimize them towards efficient wave control.

In this talk, I will first explain how generalized continuum models (especially micromorphic models) can be used to effectively describe the homogenized response of infinite-size metamaterials.

I will then introduce the concepts of non-coherent interfaces and microstructure-driven interface forces in the framework of micromorphic elasticity. I will show that such concepts are of paramount importance when studying the response of finite-size mechanical metamaterials at the homogenized macro-scale.

The need of introducing interface forces will be elucidated through numerical examples comparing the micromorphic simulations to their full-microstructured counterparts. These results provide a milestone for the understanding of finite-sized metamaterials’ modeling at the homogenized scale and for the use of micromorphic-type models to achieve an accurate upscaling towards larger-scale metamaterials’ structures.

Prof. Dr. Angela Madeo: Starting from September 2021, Angela Madeo is Full Professor of Structural Mechanics at Faculty of Architecture and Civil Engineering of TU-Dortmund (Germany).

She is Principal Investigator of the ERC Consolidator Grant META-LEGO, awarded by the European Commission with 2 million euros. In this ERC project she explores how enriched continuum models of the micromorphic type can be used to study the mechanical behavior of metamaterials and to provide a feasible transition from small-scale to larger scale metamaterial structures.

She is the Coordinator of the International Master "Mechanics of Sustainable Materials and Structures" (MS^2), offered at the Faculty of Architecture and Civil Engineering of TU-Dortmund (Germany), in Partnership with University of Trento (Italy) and Ecole Centrale Nantes (France). This International Master has been awarded by the European Commission with an Erasmus Mundus Joint Master (EMJM) funding of 4 million euros, aimed at attracting the best Civil Engineering students from all over the world.

From 2017 to 2021, she was full professor at the GEOMAS Laboratory of the Institut National des Sciences Appliquées (INSA) de Lyon (France). She has been Associate Professor at INSA Lyon from 2010 to 2017. She obtained her PhD in Theoretical and Applied Mechanics at the University of Rome “La Sapienza” in 2009. She obtained a Master of Science in Civil Engineering at the University of Rome “La Sapienza” (Italy) in 2005 and a second one in Engineering Science and Mechanichs at the Virginia Polytechnic Institute and State University (USA) in 2006.

Her research expertise seats on the study of Enriched Models in Continuum Mechanics and their applications to mechanical metamaterials, as well as to other materials with heterogeneous microstructures. She is member of the prestigious Institut Universitaire de France since 2016, when she was nominated as junior IUF member for her ground- breaking research on enriched continuum modeling of metamaterials. She was recipient of the CNRS Bronze medal in 2015.

She coordinated several research projects funded with National French grants (ANR), as well as European grants (RIA, Horizon 2020, ERC, EMJM). She co-authored more than 90 papers in high-level international journals, she is author of a book on Generalized Continuum Mechanics and Engineering Applications, edited by ISTE Editions in 2015 and she has an H-index of 44 (according to Google Scholar).

She is member of the Editorial board of 4 high level international journals in the field of Theoretical and Applied Mechanics (European Journal of Mechanics A/Solids, Wave Motion, Archive of Applied Mechanics, Mathematics and Mechanics of Solids).