A modified Lekhnitskii formalism a la Stroh for anisotropic elasticity andclassifications of the 6x6 matrix N

The Stroh formalism for two-dimensional deformations of anisotropic elastic materials computes the eigenvalue p and the eigenvector a from an eigenrel ation. The vector b is then determined from a. Depending on the number of r epeated eigenvalues p and the number of independent eigenvectors (a, b) the system has, it can be classified into six groups. The Lekhnitskii formalis m has no eigenrelation to speak of. We present a modified Lekhnitskii forma lism that computes the eigenvalue p and the eigenvector b from an eigenrela tion. The vector a is then determined from b. Thus the modified Lekhnitskii formalism is a dual to the Stroh formalism. Not only does the modified for malism enable us to do the classifications, it is much simpler than using t he Stroh formalism. The six groups are the SP, SS, D1, D2, ED and ES groups . The ES group does not exist for a real material. The SS group (that has p (1) = p(2) not equal p(3)) and the D2 group (that has p(1) = p(2) = p(3)) c an be identified without computing the eigenvalues p and the eigenvectors ( a, b). We show that the repeated eigenvalue p(1) = p(2) in the SS and D2 gr oups is simply a root of the quadratic equation l(2) = 0. We present an exp licit expression of p(3) for the SS group. The ED group that has three iden tical p can also be identified without computing p and (a, b) however, we d o present an explicit expression of p. We show that monoclinic materials wi th the symmetry plane at x(3) = 0 cannot belong to the ED group. The identi fication of the SP and DI groups is the only one that requires computation of p but not (a, b). For special classes of materials, however, they can be identified without computing p. In all cases, the eigenvectors and the gen eralized eigenvectors are obtained explicitly.