SGBEM–FEM coupling for analysis of cracks in 3D anisotropic media

Abstract

SUMMARYA weakly singular symmetric Galerkin boundary element method (SGBEM) is coupled with the standard finite element method (FEM) in order to establish an accurate and efficient numerical technique for analysis of fractures in three-dimensional, anisotropic, linearly elastic media. In the strategy, the weakly singular SGBEM developed by Rungamornrat and Mear (Int. J. Solids Struct. 2008; 45:1283-1301 Comput. Methods Appl. Mech. Engrg 2008; 197:4319-4332) is utilized to model a small-scale region containing the crack while the (possibly large and complex) compliment region is treated by the FEM. The coupled technique exploits the positive features of both methods; the SGBEM proves to be a convenient and highly accurate method for obtaining mixed-mode stress intensity factors along the crack front, whereas the FEM is very efficient for modeling large-scale problems in the absence of cracks. An important aspect of the formulation and implementation of the technique is that continuity of displacement and traction across the interface between the SGBEM and FEM regions is enforced in a weak sense. This allows the two regions (one modeled by the SGBEM and the other by the FEM) to be discretized independently without the need for the resulting meshes to conform on the interface separating the regions, and this flexibility in the discretization process leads to a significant reduction in the modeling effort. To demonstrate the utility and accuracy of the technique, several boundary value problems involving both embedded and surface breaking cracks are treated, and it is shown that the coupled technique yields highly accurate stress intensity factors that exhibit only a slight dependence upon mesh refinement.

A SFBEM–FEM coupling method for solving crack problems based on Erdogan fundamental solutions

“…( 18), one obtains a relationship between the nodal force vector and the nodal displacement vector for the cracked superelement shown in Fig. 2, which can be written as e e e  F K U (19) where e K is the stiffness matrix of the cracked superelement, which can be expressed as…”

“…However, for crack problems of complex structures with complex boundary conditions, it is not convenient to model the structures and apply the boundary conditions with BEM, and for multicrack problems, multi-domain coupling techniques are further required in BEM formulation when the single-crack Erdogan fundamental solutions are used. Therefore, in order to make full use of the unique advantage of BEM in dealing with the singular behaviour at crack tips and the superior flexibility of FEM in modelling complex structures and boundary conditions, several researchers proposed the BEM-FEM coupling methods to solve complex crack problems [15][16][17][18][19][20]. Actually, the BEM-FEM coupling techniques stem from the pioneering work of Zienkiewicz et al [21] and Brebbia and Georgiou [22], and now have appeared in the areas of flexoelectricity [23], vibroacoustic response [24], fluid-structure interaction [25] and soil-structure interaction [26], among others.…”

The Numerical Simulation Method of the Slot Crack Groups’ Effect Analysis for Solid Rocket Motor Grain

“…The new methods to solve this problem also include boundary integral equation methods (BIEMs). In recent years, BIEMs have been proven to be computationally efficient and yield accurate results for the analysis of fracture problems in both 2D and 3D settings [10][11][12][13][14][15][16].…”

Dimensional model reduction for flow through fractures in poroelastic media

“…In this work we treat stationary fractures. Fracture propagation has been modeled using level set methods [10,22], phase-field methods [33], or boundary element methods [41]. Incorporating some of these techniques into the Brinkman-Biot model is a topic of future research.…”