An improved computational framework based on the dual boundary element method for three-dimensional mixed-mode crack propagation analyses

The fracture failure of three-dimensional concrete structures subjected to concentrated loadings using the Boundary Element Method

“…Solely discontinuous boundary elements have been utilised along the crack surfaces as classically required by the dual BEM approach. Besides, the Gauss-Legendre numerical scheme handles the integration over non-singular boundary elements, in which sub-element technique improves its accuracy [23]. The singularity subtraction technique proposed by Guiggiani and Gigante [46] and Guiggiani et al [47] regularizes the kernels over singular-elements and enables the accurate assessment of singular and hypersingular BIE.…”

“…The singularity subtraction technique proposed by Guiggiani and Gigante [46] and Guiggiani et al [47] regularizes the kernels over singular-elements and enables the accurate assessment of singular and hypersingular BIE. It is worth mentioning that Cordeiro and Leonel [23] presents the regularization expressions for hypersingular kernels, which have been utilised herein.…”

“…On the other hand, the Boundary Element Method (BEM) demonstrates excellent performance in fracture problems, especially in the three-dimensional context as demonstrated by Cordeiro and Leonel [22], [23] and Mi and Aliabadi [24], [25]. The BEM does not require domain mesh, which enables accurate assessment of internal mechanical fields and non-complex remeshing procedures during the crack growth.…”

The stress intensity factor assessment in three-dimensional problems by the displacement fitting technique and the dual Boundary Element Method

“…The displacement correlation/extrapolation techniques consist of correlating or extrapolating the numerical displacement field at the crack tip with the asymptotic local displacement analytical solution. These solution techniques have been used in its classical form to extract SIFs from the finite element method (FEM) (Chan et al, 1970;Ingraffea and Manu, 1980;Banks-Sills and Sherman, 1986;Banks-Sills et al, 2005;Nejati et al, 2015) and BEM (Cruse and Wilson, 1978;Balderrama et al, 2006;Purbolaksono et al, 2012;Gonzalez et al, 2015;Cordeiro and Leonel, 2018;Cordeiro and Leonel, 2019). Recently, SIFs values have also been obtained from the extended/generalized finite element method (X/GFEM) using such scheme (Minnebo et al, 2010;Gonzalez-Albuixech et al, 2013;Schätzer and Fries, 2016;Gupta et al, 2017;Gupta and Duarte, 2018).…”

“…On the other side, the high order terms enable the proper assessment of SIFs by DFT. However, some studies in the literature report responses instabilities of displacement correlation/fitting techniques (Cordeiro and Leonel, 2019), which can be largely dependent on the extraction points. This subject is particularly handled in the present study and a parametric analysis suggests the better positions for extracting SIFs.…”