Spectral decomposition of anisotropic elasticity

Summary A newly developed approach, based on the spectral decomposition principle, which is especially useful in crystallography, is applied in this paper. The compliance fourth-rank tensor of crystalline media belonging to the monoclinic system is spectrally decomposed, its eigenvalues are evaluated, together which its elementary idempotent tensors, which expand uniquely the fourth-rank tensor space into orthogonal subspaces. Next, the compliance tensor is spectrally analysed for anisotropic media of the orthorhombic, tetragonal, hexagonal and cubic crystal systems, by regarding these decompositions as particular cases of the spectral decomposition for monolinic media. Consequently, the characteristic values and the idempotent fourth-rank tensors are derived, as well as the stress and strain second-rank eigentensors for all the above mentioned symmetries.