Bloch spectral analysis in the class of non-periodic laminates

Abstract

In this work, we introduce Bloch waves to study the homogenization process in a class of simple laminates which are obtained as a particular Hashin-Shtrikman microstructure involving translations and dilations in only one direction. This makes this class of microstructures non necessarily periodic in the direction of lamination. We derive explicit formulae for the Bloch wave spectral representation of the homogenized coefficients.

Keywords

• homogenization
• laminates
• hashin-shtrikman
• spectral analysis
• bloch waves