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

The elastic stiffness or compliance is a fourth-order tensor that can be expressed in terms of two second-order symmetric tensors A and B and a fourth-order completely symmetric and traceless tensor Z (or z). It is shown that the parts associated with A, B and Z (or z) are all structurally invariant under a three-dimensional transformation. Thus a linear combination of the three parts gives a general expression for three-dimensional structural invariants. All three-dimensional structural invariants available in the literature are shown to be special cases of this general expression. Invariants that are inherited by each structural invariant are presented.