A Westergaard-type stress function for line inclusion problems

A direct correspondence is shown to exist between the Westergaard stress function for crack problems and a newly-introduced stress function for rigid line inclusion problems. A correspondence is also shown to exist between stress intensities in the crack and the inclusion problems, as well as between the opening displacement of the crack and the axial force in the inclusion. A scheme is presented to modify these rigid-inclusion solutions to account approximately for non-zero compliance of real fibers in a composite material.