Dynamics and wave propagation in metamaterials

At LMSSC, Paris, November 6th 2024, 1.30 p.m.

Bilen Emek Abali
Associate Professor, Applied Mechanics, Department of Materials Science and Engineering, Uppsala University, Sweden

Materials with a microstructure are called metamaterials that deviate from first order theory. By using generalized mechanics, where the deformation energy depends also on the second gradient of displacement, we obtain the necessary accuracy with introducing additional metamaterial parameters. By using homogenization techniques [1, 2, 3], these parameters are obtained in statics. In the case of dynamics, we discuss several numerical problems as well as inertial parameters in metamaterials with a periodic microstructure. We provide solutions by means of the finite element method and open source packages for dynamic metamaterial simulations.

[1] B. E. Abali and E. Barchiesi. “Additive manufacturing introduced substructure and compu-tational determination of metamaterials parameters by means of the asymptotic homoge-nization”. In: Continuum Mechanics and Thermodynamics 33.4 (2021), 993–1009.

[2] B. Vazic, B. E. Abali, H. Yang, and P. Newell. “Mechanical analysis of heterogeneous materialswith higher-order parameters”. In: Engineering with Computers 38.6 (2022), pp. 5051–5067.

[3] H. Yang, B. E. Abali, W. H. Müller, S. Barboura, and J. Li. “Verification of asymptotic homog-enization method developed for periodic architected materials in strain gradient continuum”. In:International Journal of Solids and Structures 238 (2022), p. 111386.