A review of the scaled boundary finite element method for two-dimensional linear elastic fracture mechanics

Abstract

The development and the application of the scaled boundary finite element method for fracture analysis is reviewed. In this method, polygonal elements (referred to as subdomains) of arbitrary number of edges are constructed, with the only limitation that the whole boundary is directly visible from the scaling centre. The element solution is semianalytical. When applied to two-dimensional linear fracture mechanics, any kinds of stress singularities are represented analytically without local refinement, special elements and enrichment functions. The flexibility of polygonal elements in geometric shape leads to simple yet efficient remeshing algorithms to model crack propagation. Coupling procedures with the extended finite element method, meshless method and boundary element method to handle changes in the crack morphology have been established. These developments result in an efficient framework for fracture modelling. Examples of applications are provided to demonstrate their feasibility.

Convergence properties of the enriched Scaled Boundary Finite Element Method in fracture mechanics

“…Especially in the 2D case, the SBFEM has proven to be a powerful method for the treatment of cracks and stress singularities [4]. However, in 3D problems of fracture mechanics, stress singularities still occur at points where the crack front intersects the discretized boundary.…”

A Brief Review on Polygonal/Polyhedral Finite Element Methods

“…Various applications of PSBFEM can be seen in literature such as in linear elasticity [83], crack propagation [84][85][86][87][88], applications within geotechnical structures [89], dynamic fracture simulation [90], analysis of cracked functionally graded materials [91], polygonal mesh creation , elastoplastic analysis of structures [92], prediction of structural responses with randomly distributed material properties [93], simulation of crack surface contact problems 8 Mathematical Problems in Engineering [94], and analysis of mesoscale concrete samples [95]. Extension of the method to 3D can be seen in the literature [96][97][98].…”

NURBS-Enhanced Meshfree Method with an Integration Subtraction Technique for Complex Topology

“…Moreover, some three dimension problems with singular [33] or nonsingular [34] boundary element method have also been investigated. The SBEM still requires a subdomain (having the same role as an element in the finite element method) to satisfy the scaling requirement (i.e., the whole boundary is directly visible from a point) in the discretization process [35], which is still a challenge work in the adaptive problems for complex two dimension domain and even three dimension domain.…”