Decomposition of elasticity tensors and tensors that are structurally invariant in three dimensions

The elastic stiffness or compliance is a fourth-order tensorthat can be expressed in terms of two second-order symmetrictensors A and B and a fourth-order completely symmetric andtraceless tensor Z (or z). It is shown that the parts associatedwith A, B and Z (or z) are all structurally invariant undera three-dimensional transformation. Thus a linear combinationof the three parts gives a general expression for three-dimensionalstructural invariants. All three-dimensional structural invariantsavailable in the literature are shown to be special cases ofthis general expression. Invariants that are inherited by eachstructural invariant are presented.