Non-uniqueness of time-domain reflection from 3D planar elastic layers

Abstract

Recently, some explicit results were obtained regarding non-uniqueness for the traction to displacement maps of bounded elastic bodies in 2D and 3D, under the assumption of an internal kinematic constraint. The approach utilized is that of transformation optics. As the approach could, under the usual continuum assumptions, handle all frequencies without resorting to active materials, it could potentially be directly applied also to time domain problems. In the present paper we cover the extension to the time domain of these recent results in the case of reflection from a composite slab of rather general anisotropy, and derive the required material properties of different slabs with identical reflection properties. In particular we describe how homogeneous and inhomogeneous slabs of very different thicknesses may be indistinguishable with respect to elastic wave reflection properties. It should be noted that the approach retains both the minor and major symmetries of the stiffness tensor, and does not require an anisotropic mass density tensor to be used.