A nonlinear finite element eigenanalysis of singular plane stress fields in bimaterial wedges including complex eigenvalues

A finite element formulation is developed for the analysis of variable-sepa rable singular stress fields in power law hardening materials under conditi ons of plane stress. The displacement field within a sectorial element is a ssumed to be quadratic in the angular coordinate and of the power type in t he radial direction as measured from the singular point. An iteration schem e that combines the Newton method and matrix singular value decomposition i s used to solve the nonlinear homogeneous eigenvalue problem, where the eig envalues and eigenfunctions are obtained simultaneously. The formulation an d iteration scheme apply when the eigenvalue is complex. The examples consi dered include the single material crack and wedge to demonstrate convergenc e, and the bimaterial interface crack and the bimaterial wedge to demonstra te geometric versatility and the ability to handle complex eigenvalues. It is found that the real part of the complex eigenvalue for the interface cra ck agrees with the HRR value. In this case the associated complex eigenfunc tion is converted into an approximate real-valued eigenfunction that is val id for any mode-mix. In addition, the behavior of separable solutions near certain 'wedge paradox' geometries where non-separable solutions occur is i nvestigated.