Ultrasonic wave interaction with a thin anisotropic layer between two anisotropic solids: Exact and asymptotic-boundary-condition methods

Boundary conditions introduced to model a thin anisotropic layer between two generally anisotropic solids are given. The model can be used to describe an imperfect anisotropic interface. The present results for anisotropic boundary conditions are a generalization of previous work valid for either an isotropic viscoelastic layer [J. Acoust. Soc. Am. 89, 503–515 (1991)] or an orthotropic layer with a plane of symmetry coinciding with the incident plane [J. Acoust. Soc. Am. 91, 1875–1887 (1992)]. The boundary conditions are represented by a 6×6 transfer matrix which relates six-dimensional vectors formed from stresses and displacements on each side of the interface. The transfer matrix is obtained as an asymptotic representation of the three-dimensional solution for a thin orthotropic layer of arbitrary orientation between two solids. Such boundary conditions couple the in-plane and out-of-plane stresses and displacements on the interface even for isotropic bodies. Interface imperfections are modeled by an interfacial multiphase orthotropic layer with effective elastic properties. This determines the elements in the transfer matrix which includes both interface stiffness and inertial terms. The results are illustrated by numerical examples of ultrasonic wave reflection from an imperfect interface between anisotropic solids. The applicability of the boundary condition approach is analyzed by comparison with the exact solutions, which are obtained by taking into account multiple reflections inside the layer. It is shown that for small layer thickness-to-wavelength ratio, the asymptotic transfer matrix describes accurately the dynamical behavior of a thin interfacial layer between two generally anisotropic media. Interface waves are also considered and illustrated numerically.