Exact Elastodynamic Homogenization of Laminated Composites Revisited

Abstract

This paper revisits Willis' elastodynamic homogenization (Mechanics of Materials, 41 (2009) 385-393) of periodic laminate composites and uses the equivalent inclusion-based method (EIM) to evaluate the unique effective constitutive properties with eigen-fields. The microstructure-specific Green's function is essential in Willis's exact homogenization method, which was derived from the corresponding periodic laminates. Our re-examination identifies several algebraic differences in the published formulae for the Floquet number and the related effective properties. In parallel, this paper simulates inhomogeneities with a comparison medium containing two eigen-fields, namely eigenstrain and eigen-momentum, to simulate stiffness and mass density mismatch, respectively. Therefore, the general Green's function can be directly used. The exact homogenization method with the updated specific Green's function is compared to the proposed EIM with eigen-fields homogenization scheme, and excellent agreement is obtained. The present paper provides a base to extend the homogenization framework to multi-dimensional Willis-type homogenization.