The stroh formalism for anisotropic materials that possess an almost extraordinary degenerate matrix N

Abstract

It has been discovered recently that the 6 x 6 elasticity matrix N for an anisotropic elastic material under a two-dimensional deformation can be extraordinary degenerate, i.e., N can have three identical pairs of complex conjugate eigenvalues but has only one pair of complex conjugate eigenvector. The Stroh formalism and the modified formalism for a simple degenerate N available in the literature need to be revised. What is more likely to happen in applications is that the matrix N is almost extraordinary degenerate. In that case the orthonormalized eigenvectors can be very large, causing certain numerical problems. We therefore present in this paper a modified formalism that is applicable to the case when N can be extraordinary degenerate or almost extraordinary degenerate.