Semi-analytical evaluation of dynamic stress-intensity factors

The scaled boundary finite-element method, a semi-analytical boundary element method based on finite elements, is applied to the transient dynamic analysis of fracture mechanics problems. The static-stiffness matrix and the mass matrix are obtained with the scaled boundary finite-element method. The dynamic response is calculated directly in the time domain using a standard time-integration scheme. This method does not require the discretization of the straight crack faces and material interfaces passing through the crack tip. In the radial direction the displacements follow from the analytical solution without any a priori assumption. The boundary conditions on the crack faces and material interfaces are satisfied exactly. The scaled boundary finite-element method permits an accurate representation of singularities in the radial direction using analytical functions. The stress-intensity factors are calculated directly from their definitions. 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.