The improvement of crack propagation modelling in triangular 2D structures using the extended finite element method

Abstract

In this paper, a novel geometric method combined with the piecewise linear function method is introduced into the extended finite element method (XFEM) to determine the crack tip element and crack surface element. Then, by combining with the advanced mesh technique, a novel method is proposed to improve the modelling of crack propagation in triangular 2D structure with the XFEM. The numerical tests show that the accuracy, the convergence, and the stability of the XFEM can be improved using the proposed method. Moreover, the applicability of the conventional multiple enrichment scheme is discussed. Compared with the proposed method, the conventional multiple enrichment scheme has deficiency in mixed mode I and II crack. Finally, a comparative study shows that the performance of the XFEM by using the proposed method to model the crack propagation can be greatly improved.

Numerical integration in G/XFEM analysis of 2-D fracture mechanics problems for physically nonlinear material and cohesive crack propagation

“…The integrand of the weak form of the boundary value problem is no longer polynomial; hence, the Gauss integration rule generally used in FEM is unsuitable. Several alternatives have been proposed to surpass such limitation (Fries and Belytschko, 2010), and one frequently used, and herein studied, is the subdivision of elements (Mo€ es et al, 1999;Sukumar et al, 2000;Park et al, 2009;Pereira et al, 2009;Torres et al, 2015;Chen et al, 2018;Zhou and Chen, 2019).…”

Fatigue crack growth simulation using the moving mesh technique

“…11 Because of such drawbacks, the fatigue life estimation of a material component is increasingly analyzed using numerical simulations. The clear advantages provided by numerical simulations as means of analysis have led to the development of different numerical approaches for reproducing fatigue crack propagation phenomena, such as the finite element method (FEM), [21][22][23][24] the extended finite element method (XFEM), 8,[25][26][27][28] or traditional meshless methods. 29,30 The FEM is the most renowned approach to studying fatigue and fracture mechanics problems because of its widespread diffusion and simplicity in modeling complex structures and advanced solid mechanics problems.…”

“…Because of such drawbacks, the fatigue life estimation of a material component is increasingly analyzed using numerical simulations. The clear advantages provided by numerical simulations as means of analysis have led to the development of different numerical approaches for reproducing fatigue crack propagation phenomena, such as the finite element method (FEM), 21–24 the extended finite element method (XFEM), 8,25–28 or traditional meshless methods 29,30 …”

On the numerical integration in generalized/extended finite element method analysis for crack propagation problems

“…Generalized quadratures suited for elements with discontinuities were also proposed (Mousavi and Sukumar, 2010a; Mousavi and Sukumar, 2010b). Another option is to subdivide each polygonal sub-domain into triangular cells where the Gauss quadrature can be applied precisely (Moës et al , 1999; Sukumar et al , 2000; Kang et al , 2015; Kang et al , 2017; Chen et al , 2018; Nguyen et al , 2019; Zhou and Chen, 2019). Both strategies conduce to similar results, although the former is limited to two-dimensional spaces.…”