Elastic waves under unusual anisotropy

In this paper the problem of finding all elastic anisotropic materials, tha t transmit longitudinal elastic waves in exactly the same manner as isotrop ic materials, is proposed and solved. The solution is given in Theorem 1. I n such anisotropic materials elastic energy stored under any one-dimensiona l stretch does not depend on the stretching direction. In Theorem 3 a diffe rent class of anisotropic materials is described, for which the elastic ene rgy stored under pure shearing does not depend on the shear direction. Such materials transmit at least one transverse elastic wave in every direction . The tools used to solve the problems are invariant decompositions of Hook e's tensors. (C) 2001 Published by Elsevier Science Ltd.