On the stress concentration factor of circular/elliptic hole and rigid inclusion under the remote anti-plane shear by using degenerate kernels

The stress concentration factor (SCF) along the boundary of a hole and a rigid inclusion in an infinite isotropic solid under the anti-plane shear is revisited by using degenerate kernels in the boundary integral equation (BIE) although this result was obtained by invoking the extended circle theorem of Milne-Thomson as well as the complex variable approach. The degenerate kernel of series form for the closed-form fundamental solution is used for the circle and the ellipse in terms of polar and elliptic coordinates, respectively. The slender ratio of the ellipse and the orientation are two parameters for our study. The strain energy density along the boundary is increased or decreased due to the different types of loading and various aspect ratios of the ellipse. An analytical solution for the SCF is then derived for any orientation of the ellipse relative to the applied load. The reciprocal relation for the SCF between a hole and a rigid inclusion with respect to different loading is also addressed. Besides, this analytical derivation can clearly show the appearing mechanism why the BEM/BIEM suffers the degenerate scale in the rigid inclusion.