A nonlinear finite element eigenanalysis of singular stress fields in bimaterial wedges for plane strain

A displacement-based finite element formulation for the analysis of singula r stress fields in power law hardening materials under conditions of plane strain is presented. The displacement field within a sectorial element is q uadratic in the angular coordinate and of the power type in the radial dire ction as measured from the singular point. A hydrostatic pressure variable, which is linear in the angular coordinate, is introduced to account for th e incompressibility of the material. The Newton method is combined with mat rix singular value decomposition to iteratively solve the resulting nonline ar homogeneous eigenvalue problem where the eigenvalues and eigenfunctions are obtained simultaneously. The examples considered include the single mat erial wedge, the bimaterial interface crack and the bimaterial wedge. In pa rticular, the case of a single material wedge bonded to a rigid material al ong one edge is examined to study the possibility of the existence of mixed mode solutions for arbitrary wedge angles, including the important case of an interface crack when the wedge angle is 180 degrees. This behavior is d istinctly different from that of plane stress where a complex singularity i s obtained. The possibility of the existence of nonseparable solutions is a lso discussed.