Crack propagation modelling in concrete using the scaled boundary finite element method with hybrid polygon-quadtree meshes
- Authors: Ooi, Ean Tat , Natarajan, Sundararajan , Song, Chongmin , Ooi, Ean Hin
- Date: 2017
- Type: Text , Journal article
- Relation: International Journal of Fracture Vol. 203, no. 1-2 (2017), p. 135-157
- Full Text: false
- Reviewed:
- Description: This manuscript presents an extension of the recently-developed hybrid polygon-quadtree-based scaled boundary finite element method to model crack propagation in concrete. This hybrid approach combines the use of quadtree cells with arbitrary sided polygons for domain discretization. The scaled boundary finite element formulation does not distinguish between quadtree cells and arbitrary sided polygons in the mesh. A single formulation is applicable to all types of cells and polygons in the mesh. This eliminates the need to develop transitional elements to bridge the cells belonging to different levels in the quadtree hierarchy. Further to this, the use of arbitrary sided polygons facilitate the accurate discretization of curved boundaries that may result during crack propagation. The fracture process zone that is characteristic in concrete fracture is modelled using zero-thickness interface elements that are coupled to the scaled boundary finite element method using a shadow domain procedure. The scaled boundary finite element method can accurately model the asymptotic stress field in the vicinity of the crack tip with cohesive tractions. This leads to the accurate computation of the stress intensity factors, which is used to determine the condition for crack propagation and the resulting direction. Crack growth can be efficiently resolved using an efficient remeshing algorithm that employs a combination of quadtree decomposition functions and simple Booleans operations. The flexibility of the scaled boundary finite element method to be formulated on arbitrary sided polygons also result in a flexible remeshing algorithm for modelling crack propagation. The developed method is validated using three laboratory experiments of notched concrete beams subjected to different loading conditions.
Dynamic fracture simulations using the scaled boundary finite element method on hybrid polygon-quadtree meshes
- Authors: Ooi, Ean Tat , Natarajan, Sundararajan , Song, Chongmin , Ooi, Ean Hin
- Date: 2016
- Type: Text , Journal article
- Relation: International Journal of Impact Engineering Vol. 90, no. (2016), p. 154-164
- Full Text: false
- Reviewed:
- Description: In this paper, we present an efficient computational procedure to model dynamic fracture within the framework of the scaled boundary finite element method (SBFEM). A quadtree data structure is used to discretise the domain, and 2:1 ratio between the cells is maintained. This limits the number of patterns in the quadtree decomposition and allows for efficient computation of the system matrices. The regions close to the boundary are discretised with arbitrary sided polygons so as to facilitate accurate modelling of the curved boundaries. The stiffness and the mass matrix over all the cells are computed by the SBFEM. Moreover, the semi-analytical nature of the SBFEM enables accurate modelling of the asymptotic stress fields in the vicinity of the crack tip. An efficient remeshing algorithm that combines the quadtree decomposition with simple Boolean operations is proposed to model the crack propagation. The remeshing is restricted only to a small region in the vicinity of the crack tip. The efficiency and the convergence properties of the proposed framework are demonstrated with a few benchmark problems. © 2015 Elsevier Ltd. All rights reserved.