Wave propagation in periodic microstructures by homogenisation of extended continua

The present contribution deals with the derivation of dispersion relations for a periodic grid structure in terms of a micropolar mean-field theory. For that purpose, the constitutive equations of the effective continuum are computed with the aid of a two-level Finite Element scheme. The equations of motion are evaluated for plane harmonic waves and the resulting dispersion relations are compared to that one of an isotropic micropolar medium.