Sextic formalism in anisotropic elasticity for almost non-semisimple matrix N
The sextic formalism of Stroh for anisotropic elasticity [\textit{A. N. Stroh}, J. Math. Phys. 41, 77-103 (1962; Zbl 0112.168)] leads to the eigen-relation \(N\xi =p\xi\) in which N is a \(6\times 6\) real matrix. The orthogonality and closure relations as well as many other relations involving the eigenvalues p and the eigenvectors \(\xi\) are based on the assumption that N is simple or semisimple so that the six eigenvectors \(\xi_{\alpha}\) span a six-dimensional space. Problems arise when N is non-semisimple. In fact there are problems even when N is almost non- semisimple. We present a modified formalism which is valid regardless of whether N is simple, almost non-semisimple or non-semisimple. The modified formalism does not apply when N is semisimple.
scientific article; zbMATH DE number 4016293