Analytical expression of TI elastic tensor with arbitrary orientation
任意空间取向TI弹性张量解析表述

In this paper the analytical expression for elastic tensor of TI with arbitrary orientation (ATI) is given that has coefficients as combination of elastic constants of VTI and includes isotropic term, quadratic and fourth-order terms of the direction vector components of TI symmetry axis. Such direction vector of TI symmetry axis could be defined in the fixed coordinates, can also be relative to three dimensional boundaries of the media and even to wave propagation direction. In comparison with fourth order tensor transformation and Bond transformation, ATI elastic tensor can provide all its components in the constitutive relation and wave motion equation concisely and transparently for theoretical investigation in many aspects.