A new formulation of SBFEM and its application to SIF computation of 3D crack

Abstract

This paper presents a novel scaling line center based scaled boundary finite element method for accurately computing stress intensity factors in three-dimensional fracture problems. Traditional methods, such as the finite element method and the boundary element method, often necessitate mesh refinement near crack fronts, which can result in computational inefficiencies and potential inaccuracies. Although scaled boundary finite element method provides advantages in addressing crack tip singularities, its existing formulations depend on a single scaling center point, which imposes geometric constraints and reduces accuracy in complex crack geometries. The proposed scaling line center based scaled boundary finite element overcomes these limitations by taking the crack front as a scaling line center, characterizing the singularity of stress field and improving accuracy of the computation of the stress intensity factor. The proposed methodology is theoretically formulated within a Hamiltonian framework and rigorously validated through a series of benchmark problems, including: (1) a cantilever beam subjected to concentrated loading, (2) single-edge crack specimens under both uniaxial tension and shear loading conditions, and (3) a lens-shaped crack embedded in a cubic domain under hydrostatic tension. Its ability to efficiently model complex three-dimensional cracks make it a valuable method for structural integrity assessment and failure analysis in fracture mechanics.