Computation of 3-D stress singularities for multiple cracks and crack intersections by the scaled boundary finite element method

Abstract

Among the various possible ways of dealing with notch and crack situations, the scaled boundary finite element method [SBFEM, (Wolf and Song in Finite element modelling of unbounded structures. Wiley, Chichester, 1996; Wolf in The scaled boundary finite element method. Wiley, Chichester, 2003)]has been adopted in this work. This method has been proved to be versatile, much less time consuming than the finite element method and generates highly accurate numerical predictions in cases of structures with notches and cracks. The SBFEM gives the advantage of boundary element method by reducing one dimension in modelling the structures but the mathematical formulations are more related to conventional displacement based finite element method. This method requires a certain scalability of the given structure with respect to a point called similarity center. Like in the case of the boundary element method, the structure needs to be discretized only at the surface where standard displacement based isoparametric finite element formulations are adequate. Unlike in the boundary element method, however, no fundamental solution is required by the scaled boundary finite element method. The similarity or scalability of the method requires separation of coordinates such that in the radial direction (i.e. scaling direction) it yields simple differential equations that can be solved analytically. So this approach can be considered as a semi-analytical method. Several two-dimensional examples have been analysed for crack and notch situations that are well known cases in fracture mechanics. A number of three-dimensional cases have been considered for different crack configurations that yield high order of singularity. The results, according to the authors' knowledge are up to now unpublished in the open literature. Parametric studies are conducted for structures with bi-material interfaces.

Overview of Structural Life Assessment and Reliability, Part I: Basic Ingredients of Fracture Mechanics

“…On the other hand, in the boundary-element method, the spatial dimension is reduced by one as only the boundary is discretized with surface finite elements, reducing the data preparation and computational efforts, that the boundary conditions at infinity are satisfied exactly, and that no approximation other than that of the surface finite elements on the boundary is introduced. Sev-eral two-dimensional examples were analyzed by Goswami and Becker (2012) for crack and notch situations. A number of threedimensional cases was considered for different crack configurations that yield a high order of singularity.…”

2D fracture analysis of magnetoelectroelastic composites by the SBFEM

“…The application of the SBFEM for 3D analysis is limited. Goswami and Becker [33] extended the SBFEM to analyze the stress singularities of crack interactions in sphere. So far, the stress intensity factors of 3D crack problems in general geometry have not been reported yet.…”

Finite fracture mechanics analysis using the scaled boundary finite element method

“…For example, Mittelstedt and Becker [32] developed the SBFEM for problems involving 3D notches, cracks and laminated plates. More recently, the SBFEM solution of the singularity of the Fichera's corner and sphere with crack intersection problems have been reported by Goswami and Becker [33]. This paper is limited to problems involving 2D crack initiation only.…”