An Eigensystem Approach to the Low-wavenumber Expansion of Willis' Effective Constitutive Relations in Periodic Media

Tuesday, February 21, 2017 - 11:00am - 12:00pm
Lind 305
Shixu Meng (University of Minnesota, Twin Cities)
Willis proposed effective constitutive relations applicable to the mean wave motion in composites with periodic microstructure. The focus of this work is to represent Willis' (effective) constitutive relations using an eigensystem approach and to explore their applications. We show that Willis' (effective) constitutive relations are well-defined. The effective constitutive relations are capable to capture the exact effective impedance. We established a connection between the effective impedance obtained from Willis' non asymptotic approach and the one obtained from the two scale homogenization approach. We study the high order asymptotics of the (effective) constitutive relations. The effective constitutive relations display symmetry properties and demonstrate the phenomenon of anisotropic wave dispersion. Finally we provide numerical experiments on the (effective) constitutive relations in both one dimension and two dimensions.