Dedicated to the 120th anniversary of Peter the Great St. Petersburg Polytechnic University ABSTRACTS St. Petersburg 2019 XLVII International Conference “Advanced Problems in Mechanics” June 24-29, 2019, St. Petersburg, Russia APM 2019 BOOK OF ABSTRACTS WWW.APM-CONF.SPB.RU PARAMETER DETERMINATION OF METAMATERIALS IN GENERALIZED MECHANICS VIA COMPUTATIONAL HOMOGENIZATION Abali B.E.1, Yang H.1, Papadopoulos P.2 1 - Technische Universitat Berlin, Institute of Mechanics 2 - University of California, Berkeley, Department of Mechanical Engineering
[email protected] In continuum mechanics, conventional theory of elasticity fails to model structures, where the inner substructure starts affecting the material response. An intuitive explanation for this phenomenon relies on the length scale of the geometry, macroscale, and the inner substructure, microscale. As the ratio of macroscale with respect to the microscale approaches one, and as both length scales lead to the same order, the effects of the substructure shall be incorporated and we call this structure related material system metamaterial. Modeling of metamaterial incorporates additional parameters and it is indeed possible to do computations by using the finite element method [1], [2], [3], as long as we know all parameters. Therefore, we need an approach leading to a unique determination of all parameters. For an isotropic and centrosymmetric metamaterial, there are seven parameters to determine. It is challenging to define experimental studies for obtaining all of these parameters. As these parameters result after a homogenization approach by involving the inner substructure, we can acquire these parameters purely based on computations at the microscale. By using the finite element method for detailed computations at the microscale for seven distinct cases, we masterfully generate a way to determine the seven material parameters uniquely [4].