Bloch Wave Homogenization Relative to a Microstructure

In this work, we study the aspect of Bloch wave homogenization of the new notion of convergence of microstructures represented by matrices $B^{ϵ}$ related to the classical $H$-convergence of $A^{ϵ}$ introduced in \cite{TG-MV-1}. The new macro quantity B^{#} appears to incorporate the interaction between the two microstructures $A^{ϵ},B^{ϵ}$. Here we present its Bloch spectral representation along with the homogenization result.