Floquet wave homogenization of periodic anisotropic media

A dynamic homogenization method based on Floquet wave theory is developed. The theory is based on the equivalency within the homogenization domain of Floquet waves in a periodic anisotropic medium and plane waves in a dispersive homogeneous anisotropic medium. A simple procedure has been developed to estimate analytically critical angles and the upper frequency bound of this homogenization domain. Using this method, the frequency dependent effective elastic constants are obtained and examples for [0/90] and [0/45/90/-45] composites are given. By comparison with an exact theory, it is shown that the time domain signal propagation in a periodic laminate is well described by the Floquet wave homogenization theory in the homogenization domain. It is also shown that in the static limit the results are identical to those calculated by static homogenization theory (the generalized method of cells). The potential applications of the method are discussed.