Armour College of Engineering’s Department of Mechanical, Materials, and Aerospace Engineering will welcome Dr. Marc Geers, a full professor at the Department of Mechanical Engineering of the Eindhoven University of Technology, the Netherlands, to present a lecture, “Multiscale Analysis and Homogenization of Mechanical and Dynamical Metamaterials.” This seminar is a part of the Midwest Mechanics Series.

The seminar will take place on Wednesday, April 27, 2022, from 12:45–1:45 p.m. in RE-104.

Contact Elena Magnus at magnus@iit.edu for the seminar details.

Abstract
Engineering analyses of structures and devices call for efficient numerical methods that accurately capture the behavior of the constituting materials. For highly heterogeneous materials, homogenization methods substitute the heterogeneous microstructure by an effective continuum that can be solved at the engineering level. Among the plethora of homogenization methods, computational homogenization constitutes a powerful tool to establish a two-scale coupling of complex nonlinear materials. Whereas the method has been used for a variety of problems, a new challenge arises when metamaterials are considered. Metamaterials reveal microstructures that induce a pronounced emergent effect at the macro-scale. This lecture focuses on the advanced homogenization of dynamical and mechanical metamaterials.

Dynamical metamaterials are for instance used for inhibiting sound and vibration transmission in a wide frequency range. First, a computational homogenization scheme applicable to resonant acoustic metamaterials will be outlined [1]. Exploiting linearity, a closed form micromorphic continuum homogenization approach for this class of materials is obtained. The corresponding dispersion spectra are accurately captured, and the solution of initial boundary value problems is thereby at reach. As a special case of dynamical metamaterials, metafoams will be presented [2]. Metafoams are a special class of foams combining thermo-viscous dissipation with local resonance. Direct numerical simulations and the homogenization of these metafoams (extracting relations between microstructure and effective properties) are demonstrated.

Spatial micro-scale fluctuation fields also emerge in mechanical metamaterials, driven by elastic instabilities. Mechanical metamaterials do not trivially satisfy the classical scale separation principle that underlies conventional homogenization strategies. Upon loading, these microstructures develop fine scale fluctuation patterns that directly influence the coarse scale behaviour. Exploiting a kinematical ansatz that incorporates the microstructural patterns, a micromorphic continuum is recovered [3]. The two-scale predictive capabilities of the emerging micromorphic continuum are illustrated, along with several demonstrative examples.

For both classes of metamaterials, the key aspects of the developed different homogenization methods and the resulting (emergent) continua will be highlighted.

REFERENCES
1. [1] A. Sridhar, V.G. Kouznetsova, M.G.D. Geers, “Homogenization of locally resonant acoustic metamaterials towards an emergent enriched continuum”, Comp. Mech., 57, 423-435 (2016).
2. [2] M.A. Lewinska, V.G. Kouznetsova, J.A.W. van Dommelen, M.G.D. Geers, “Computational homogenisation of acoustic metafoams”, Eur. Jnl. Mech. A/Solids, 77, article 103805 (2019).
3. [3] O. Rokos, M.M. Ameen, R.H.J. Peerlings, M.G.D. Geers, “Extended micromorphic computational homogenization for mechanical metamaterials exhibiting multiple geometric pattern transformations”, Extreme Mechanics Letters, 37, article 100708 (2020).
Note: The research is conducted in collaboration with Varvara Kouznetsova, Ondrej Rokoš, Hans van Dommelen and Ron Peerling.

Biography
Marc Geers is full professor in Mechanics of Materials at the Eindhoven University of Technology in the Netherlands since 2000. His research interests are in the field of micromechanics, multi-scale mechanics, damage mechanics and mechanical metamaterials. He published more than 250 journal papers, with a significant citation impact (Google scholar h-index=73). In the past 10 years, he presented more than 15 plenary lectures at international conferences and over 50 keynote and invited lectures. At present, he is Editor-in-Chief of the European Journal of Mechanics A/Solids and serves on the Editorial Boards of more than 15 international journals. He serves the Dutch scientific community and organizations in various responsible roles. He is a Fellow of the European Mechanics Society and a Fellow of the International Association for Computational Mechanics. He received an Advanced Grant of the European Research Council in 2013. He is the President of the European Mechanics Society EUROMECH.