Elastic Equilibrium of a Space Containing a Thin Curved Elastic Inclusion in Longitudinal Shear

Abstract

We study the problem of antiplane deformation of an isotropic medium containing a thin elastic curved inhomogeneity. The methods used for the solution of this problem are based on the application of the method of jump functions and the conditions of interaction of the matrix containing a thin curvilinear inclusion and the solution of the resultant system of singular integral equations with Cauchy-type kernels by the collocation method. Numerous examples are considered. The results of evaluation of the stress intensity factors for a crack and an absolutely rigid inclusion along a circular arc are compared with the corresponding analytic results. For a crack along a symmetric parabolic arc, the stressed state is thoroughly investigated. We also study the influence of the modulus of elasticity and the shape of the curvature of inhomogeneity (circular arc, parabola, or a half of a cosine curve) on the generalized stress intensity factors. It is shown that, for the stress intensity factors near the tip of the inhomogeneity, the inclination of the tangent at the tip to the plane of application of the shear forces is of determining importance.