Evaluation of dynamic stress intensity factors and T-stress using the scaled boundary finite-element method

A technique to evaluate the dynamic stress intensity factors and T-stress is developed by extending the scaled boundary finite-element method. Only the boundary of the problem domain is discretized. The inertial effect at high frequencies is modeled by a continued fraction solution of the dynamic stiffness matrix without introducing an internal mesh. Standard time-stepping scheme is applied to perform response history analyses directly in the time domain. The internal displacement field is obtained by numerical integration after removing the stress singularity. The dynamic stress intensity factors and the T-stress are evaluated directly based on their definitions. No asymptotic solution around the singular point is required. Numerical examples of cracks in homogeneous and bi-material plates demonstrate the simplicity and accuracy of this technique.