SEXTIC FORMALISM IN ANISOTROPIC ELASTICITY FOR ALMOST NON-SEMISIMPLE MATRIX-N

The sextic formalism of Stroh for anisotropic elasticity leads to the eigen-relation N xi equals p xi in which N is a 6 multiplied by 6 real matrix. The orthogonality and closure relations as well as many other relations involving the eigenvalue 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.