Semi-analytical representation of stress singularities as occurring in cracks in anisotropic multi-materials with the scaled boundary finite-element method

The scaled boundary finite-element method, a semi-analytical boundary-element method based on finite elements, is applied to fracture mechanics problems. Only the actual boundary of the body, but not the straight crack faces and material interfaces passing through the crack tip, is spatially discretized with finite elements, leading to a reduction of the spatial dimension by one. In the radial direction the displacements follow from the analytical solution without any a priori assumption. The boundary condition on the crack faces and material interfaces are satisfied exactly. In this boundary-element method based on finite elements, no fundamental solution is required, which permits an efficient analysis of anisotropic material and avoids singular integrals. The scaled boundary finite-element method thus permits an accurate representation of singularities in the radial direction using analytical functions.