Marc Geers’ KEYNOTE seminar “Homogenization of dynamical and mechanical metamaterials”
Tid: To 2020-10-08 kl 16.15 - 17.30
Föreläsare: Marc Geers, Eindhoven University of Technology, the Netherlands
Abstract. Engineering analyses of structures and devices call for efficient numerical methods that accurately capture the behaviour of its constituting materials. For highly heterogeneous materials, homogenization methods seek to replace the heterogeneous microstructure by an effective continuum that can be easily solved at the engineering level. Among the plethora of homogenization methods, computational homogenization constitutes a powerful tool to establish a two-scale coupling or 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 strong emergent effect at the macro-scale. This webinar focuses on our recent progress in the homogenization of dynamical and mechanical metamaterials. First, a computational homogenization scheme applicable to resonant acoustic metamaterials will be outlined. Exploiting linearity, a closed form micromorphic continuum homogenization approach for this class of materials can be obtained. The corresponding dispersion spectra are accurately captured, and the solution of initial boundary value problems is thereby at reach. A more advanced homogenization ansatz that covers Bragg scattering as well, will be presented next. Spatial micro-scale fluctuation fields also emerge in mechanical metamaterials, driven by elastic instabilities. Exploiting a kinematical ansatz that incorporates the microstructural patterns, a micromorphic continuum is recovered. The key aspects of the different homogenization methods and the resulting (emergent) continua will be highlighted, whereby several examples will be shown for the different cases presented.