Modeling Crack Propagation with the Extended Scaled Boundary Finite Element Method based on the Level Set Method


The extended scaled boundary finite element method (X-SBFEM) based on the level set method (LSM) is proposed in this paper to combine the advantages of the scaled boundary finite element method (SBFEM) and the extended finite element method (XFEM). The level set method (LSM) algorithm is applied to further develop the X-SBFEM, especially for the crack propagation problem. The Heaviside enrichment function is used to represent a jump across a discontinuity surface in a split element, and the non-smooth behavior around the crack tip is described using the semi-analytical SBFEM. The stiffness of the region containing the crack tip is computed directly, and the generalized stress intensity factors of many types of singularities are obtained directly from their definitions using consistent formulas. In the numerical simulations, a square plate with an edge crack under tension, a three-point bending beam, a four-point shear beam and a dam (the Koyna dam) with a single propagating crack are modeled. The results show that the proposed X-SBFEM is capable of calculating the stress intensity factors of cracks and predicting crack trajectories and load-displacement relations accurately. An analysis of the sensitivity of the parameters is employed to demonstrate that various mesh densities and crack propagation step lengths led to consistent results.


Civil, Architectural and Environmental Engineering


This research was supported by Grant 51121005 from the Science Fund for Creative Research Groups of the National Natural Science Foundation of China, Grant 51138001 from the State Key Program of National Natural Science Fund of China, Grant 2013zx06002001-09 from the National Grand Science and Technology Special Project of China, and Grant DUT15TD17 from the Fundamental Research Funds for the Central Universities

Keywords and Phrases

Brittle fracture; Crack propagation; Crack tips; Cracks; Drop breakup; Fracture mechanics; Hydrogels; Level measurement; Numerical methods; Plates (structural components); Stress intensity factors; Stresses; Structural analysis; Boundary finite element methods; Extended finite element method; Generalized stress intensity factors; Level Set method; Linear elastic fracture mechanics; Load-displacement relation; Scaled boundary finite element method; Three point bending beam; Finite element method; Crack propagation; Extended scale boundary finite element method; Stress intensity factors

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