Keywords: scaled boundary finite element method, finite element method, multiple crack propagation, discrete crack model, cohesive crack, fracture.

The scaled boundary finite element method (SBFEM) [1] is a semi-analytical method that is very efficient in solving problems with unbounded media, discontinuities and singularities. Yang et al. [2,3] recently extended the SBFEM to model cohesive crack propagation. They demonstrated that the SBFEM alleviates many of the problems associated with the finite element method (FEM) in modelling crack propagation. Fine crack-tip meshes or special crack tip elements are not required since accurate stress intensity factors (SIFs) can be directly extracted from the semi-analytical stress solutions and fracture problems can be modelled with substantially fewer degrees-of-freedom because only the subdomain boundaries are discretized. This simplifies the remeshing and considerably reduces computational cost.

The SBFEM-based methods developed in [2,3] are particularly suitable for problems with single crack or a few cracks. For problems with many cracks that become too close during propagation, the remeshing operation is cumbersome because the subdomains may become so distorted that not all the nodes are visible from their scaling centres. To tackle this problem, a novel hybrid method that combines the FEM and the SBFEM is developed. It exploits the flexibility of the FEM in remeshing multiple cracks and the efficiency of the SBFEM in extracting accurate SIFs directly from the semi-analytical solutions. These objectives are achieved by employing a simple, yet flexible local remeshing procedure that is entirely based on the FEM to propagate the cracks, and then replacing any existing crack tip elements with SBFEM rosettes. The coupling between the SBFEM rosettes and their surrounding elements requires no special techniques since the SBFEM subdomains are naturally compatible with the finite elements. The stiffness matrices of both the SBFEM and the FEM are assembled as in the FEM, treating the SBFEM subdomains as super elements. The cohesive cracks are modelled using cohesive interface elements that are automatically inserted into the FE mesh as the cracks propagate.

The feasibility of the hybrid method is demonstrated by modelling multiple cohesive crack propagation in a double edge notched concrete beam. The load-deflection response, crack propagation process and final crack pattern show good agreement with experimental and numerical benchmarks available in literature.

1

C. Song, J.P. Wolf, "The scaled boundary finite-element method - alias consistent infinitesimal finite-element cell method - for elastodynamics", Computer Methods in Applied Mechanics and Engineering, 147(3-4), 329-355, 1997. doi:10.1016/S0045-7825(97)00021-2

2

Z.J. Yang, A.J. Deeks, "Fully-automatic modelling of cohesive crack growth using a finite element-scaled boundary finite element coupled method", Engineering Fracture Mechanics, 74, 2547-2573, 2007. doi:10.1016/j.engfracmech.2006.12.001

3

E.T. Ooi, Z.J. Yang, "Modelling multiple cohesive crack propagation using a finite element-scaled boundary finite element coupled method", Engineering Analysis with Boundary Elements, 33, 915-929, 2009. doi:10.1016/j.enganabound.2009.01.006

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