Eigenfunction expansion solutions for three-dimensional rigid planar inclusion problems

An eigenfunction expansion method is presented to obtain three-dimensional asymptotic stress fields in the vicinity of the front of a semi-infinite infinitely rigid inclusion, subjected to the far-field antiplane shear and extension/bending loadings. Four different rigid inclusion side-surface boundary conditions are considered: (i) anticrack or perfectly bonded rigid inclusion, (ii) transversely rigid inclusion (longitudinal slip permitted), (iii) rigid inclusion in part perfectly bonded, the remainder with slip, (iv) rigid inclusion located alongside a crack. The computed stress singularity for an anticrack is the same as its plane strain counterpart, while the expression for the stress intensity factor varies in the thickness direction.