Elastic waves under unusual anisotropy

摘要

In this paper the problem of finding all elastic anisotropic materials, that transmit longitudinal elastic waves in exactly the same manner as isotropic materials, is proposed and solved. The solution is given in Theorem 1. In such anisotropic materials elastic energy stored under any one-dimensional stretch does not depend on the stretching direction. In Theorem 3 a different class of anisotropic materials is described, for which the elastic energy stored under pure shearing does not depend on the shear direction. Such materials transmit at lest one transverse elastic wave in every direction. The tools used to solve the problems are invariant decompositions of Hooke's tensors.