A novel modification of decouple scaled boundary finite element method in fracture mechanics problems

In fracture mechanics and failure analysis, cracked media energy and consequently stress intensity factors (SIFs) play a crucial and significant role. Based on linear elastic fracture mechanics (LEFM), the SIFs and energy of cracked media may be estimated. This study presents the novel modification of decoupled scaled boundary finite element method (DSBFEM) to model cracked media. In this method, only the boundaries of problems are discretized using specific higher-order sub-parametric elements and higher-order Lagrange polynomials as mapping functions. Implementing the weighted residual method and using Gauss-Lobatto-Legendre numerical integration yield diagonal Euler’s differential equations. The chief modifications among the research conducted and the previous studies concerning DSBFEM is that here in, generation of geometry process of the functional interpolation, integration of the diverse is chosen, and by current technic, the difficulty of the DSBFEM is decreased. Therefore, when the local coordinates origin is located at the crack tip, the geometry of crack problems are implemented directly without further processing. Validity and accuracy of the proposed method are fully illustrated through three benchmark problems, whose results agree very well with those of other numerical and/or analytical solutions existing in the literature.