An application of two-state M-integral for computing the intensity of the singular near-tip field for a generic wedge

Abstract

The two-state M-integral is applied for computing the intensity of the singular near-tip field around the vertex of a generic composite wedge. The eigenfunction expansion is used together with an energetics argument associated with the M-integral to show that a complementary eigenfield exists for every eigenfunction in a generic wedge. The proposed computational scheme is effective in finding the complete eigenfunction expansion, including the dominant singular terms along with the higher order terms as well. The present method is highly efficient and simple to use: the near-field information for the singular elastic boundary layer can be extracted from the far-field data without having to deploy singular finite elements for the wedge vertex. An exemplary case is illustrated by the re-entrant edge of a thin-film segment bonded to a substrate. The local stress intensity at the re-entrant vertex is obtained in terms of the shear stress intensity based upon the membrane model for the thin film on the substrate.