Computing stress singularities in transversely isotropic multimaterial corners by means of explicit expressions of the orthonormalized Stroh-eigenvectors

Abstract

Composite materials reinforced by unidirectional long fibers behave macroscopically as homogeneous transversely isotropic linear elastic materials. A general, accurate and computationally efficient procedure for the evaluation of singularity exponents and singular functions characterizing singular stress fields in multimaterial corners involving this kind of material is presented in this paper. To take full advantage of the sextic Stroh formalism of anisotropic elasticity applied to this particular problem, the complete set of explicit expressions of the eigenvalues and eigenvectors of the real 6 × 6 fundamental elasticity matrix N has been deduced for all the non-degenerate and degenerate (repeated roots of the sextic Stroh equation) cases. These expressions will also facilitate further applications of the Stroh formalism to these materials. Several numerical examples of singularity analysis of multimaterial corners appearing in adhesively bonded joints and damaged cross-ply laminates of composite materials are presented.