SOME IDENTITIES AND THE STRUCTURE OF N-I IN THE STROH FORMALISM OF ANISOTROPIC ELASTICITY

The Stroh formalism of anisotropic elasticity leads to a 6 multiplied by 6 real matrix N that can be composed from three 3 multiplied by 3 real matrices N//i (i equals 1,2,3). The eigenvalues and eigenvectors of N are all complex. New identities are derived that express certain combinations of the eigenvalues and eigenvectors in terms of the real matrices N//i and the three real matrices H, S, L introduced by D. M. Barnett and J. Lothe. It is shown that the elements of N//1 and N//3 have simple expressions in terms of the reduced elastic compliances. The authors prove that minus N//3 is positive semidefinite and, with this property, they present a direct proof that L is positive definite.