Elastic equilibrium of space with a curved thin elastic inclusion under longitudinal shear (Q2808380)

The authors study the anti-plane deformation problem for an isotropic medium with a curved thin elastic heterogeneity. The solution technique is based on the application of the method of jump functions and conditions of matrix interactions with a curved thin inclusion and solving the resulting system of singular integral equations with Cauchy kernels by the collocation method. Several examples are considered. The results of computing the stress intensity factors for a crack and absolutely rigid inclusion along the arc of a circle are compared with the corresponding analytical results. For the cracks along a symmetric arc of a parabola, the stress state is studied in detail. Also, influence of the elastic modulus and the form of heterogeneity (arc of a circle, parabola, half-cosine) on the generalized stress intensity factors is studied. It is found that the slope of a tangent at the tip, with respect to the plane of shift efforts, is essential for the stress intensity factors at the tip of the heterogeneity.