Mathematical methods for the characterization of ultrasound in anisotropic materials

Although the fundamental equations for the propagation of elastic and acoustic waves in aniotropic materials have not changed in more than a 100 years. the last few decades have seen a surge in interest in lhe topic. Much of this interest stems from the growing need for characterization of an inereasing number of exotic materials. The intent of this paper is to review, for the benefit of beginning researchers in acoustics and ultrasonics, the fundamental phenomena related to elastic wave propagation in anisoiropie media. We also present the most common and interesting theoretical methods developed over the past 20 years to model bulk wave propagation in such media. The methods discussed include plane wave superpositions, ray asymptotic theory, paraxial beams, and Greenʹs functions. More peripheral issues, including anisoiropie effects combined with various other exotic effects, are dealt with in the bibliography.