Deconstructing plane anisotropic elasticity: Part II: Stroh’s formalism sans frills

Eigensolutions for all types of anisotropic elastic materials are obtained in terms of the eigenvalues and the anisotropic elastic stiffness. The generalized eigenvectors and eigensolutions in the degenerate and extra-degenerate cases are obtained by the derivative rule. A complete set of unnormlized eigenvectors, now given in terms of the elastic moduli, define the Barnett–Lothe tensors by the same expressions irrespective of material degeneracy. Explicit expressions of the Barnett–Lothe tensors are obtained in various forms depending on the multiplicity of eigenvalues. These expressions complement the alternative expressions of Part I in terms of the elastic compliances. A new family of extra-degenerate materials is found, suggesting the superabundance of such materials. A concise proof of the equivalence of the eigensystems of the compliance-based and elasticity-based formalisms is given. Eigenrelations applicable to all cases of material degeneracy are presented in both three-dimensional and six-dimensional matrix formalisms.