Three-dimensional dynamic fracture analysis using scaled boundary finite element method: A time-domain method

Abstract

A time-domain method for modeling three-dimensional transient dynamic fracture problems is developed based on the scaled boundary finite element method (SBFEM). For this purpose, a cracked polyhedron modeled by the SBFEM is constructed to simulate the through-thickness crack in the domain. The mass and stiffness matrices of polyhedrons are derived and assembled to form the three-dimensional elastodynamic equations in the time domain. High-order elements are used to improve computational accuracy. The dynamic response is evaluated by the Newmark method, and the stress field is expressed semi-analytically. Based on the theory of linear ealstodynamic fracture mechanics, the static stress intensity factors are extended to the dynamic stress intensity factors (DSIFs) by considering the dynamic effect. The DSIFs are directly extracted from the analytical solution in the radial direction of the cracked polyhedron. Numerical examples are modeled to validate the presented method. Good agreement is observed between the computed results and the published results in the literature. The effects of the time step, mesh density, and material damping coefficient on the computational accuracy are also investigated. It is found that moderately sized third-order elements can lead to very good solutions, and an increase of both the orders or number of elements does not significantly improve the accuracy of the simulation. The distribution of the DSIFs along the crack front of the 3D models is investigated and it is found that the DSIFs vary strongly along the crack front.