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In this paper, we use spectral methods to introduce Bloch waves for studying the homogenization process in the non-periodic class of generalized Hashin–Shtrikman micro-structures (see Ref. 35), which incorporates both translation and dilation with a family of scales, including one subclass of laminates. We establish the classical homogenization result by providing the spectral representation of the homogenized coefficients. It offers a new lead towards extending the Bloch spectral analysis to general micro-structures, including the class of non-periodic media or the homogenization of Heisenberg operators (see Refs. 8 and 9).

Bloch wave spectral analysis in the class of generalized Hashin–Shtrikman micro-structures