Elastic wave propagation in noncentrosymmetric, isotropic media: Dispersion and field equations

It has been recently demonstrated by us that acoustic waves in solids can discriminate between a chiral scatterer and its mirror image. Thus, it is possible to construct an acoustically chiral composite medium by embedding chiral microstructures in a host medium. The microstructure size should be large enough compared to the shear wavelength in the matrix medium so that an incident wave can sense its handedness; at the same time, the microstructure size should be small enough that, at least in some frequency range, the composite structure should appear to be effectively chiral. Isotropic composite media with chiral microstructure can be modeled as hemitropic micropolar elastic solids, which have been the subject of some recent investigations. The simplest possible constitutive equations have been obtained, and the dispersion equations have been derived and studied. Approximate solutions of the inhomogeneous field equations have also been derived using dyadic algebra.