Multiscale mechanics of dynamical metamaterials

This contribution focuses on the computational multi-scale solution of wave propagation phenomena in dynamic metamaterials. Taking the Bloch-Floquet solution for the standard elastic case as a point of departure, an extended scheme is presented to solve for heterogeneous visco-elastic materials. The physically and geometrically nonlinear case is addressed through a transient computational homogenization scheme. In the particular case of an elastic heterogeneous microstructure, the homogenization scheme can be reduced to the computational analysis of a fluctuation-enriched extended continuum