Three-Dimensional Crack Analysis using X-FEM Considering Symmetric Conditions

Abstract

The extended finite element method (X-FEM), which can model the domain without explicitly meshing the crack surface, can be used to perform stress analyses for efficiently solving fracture mechanics problems. In the present study, the constraint condition enforcement for X-FEM analysis considering symmetry is presented. Since the interpolation functions utilized in X-FEM analysis include the enrichment basis functions, the freedoms of the node on the symmetric plane should be constrained properly in the X-FEM model with symmetric conditions. Moreover, evaluation of the energy release rate by the domain integral method should be performed considering the symmetry conditions. In the present paper, the constraint conditions for three-dimensional X-FEM analysis considering symmetric conditions are summarized, and numerical examples using symmetric X-FEM models are shown. The proposed procedure can be used to perform efficient X-FEM analyses of practical fracture problems.Key words: Extended FEM, Fracture Mechanics, Energy Release Rate, Symmetric Conditions IntroductionThe extended finite element method (X-FEM)(1)-(3) can approximate the discontinuous displacement field near cracks independently of the finite element mesh by using the interpolation functions, which can describe the displacement field near cracks in structures. Therefore, the crack modeling for stress analyses can be performed more easily by X-FEM, as compared to conventional FEM. As the information with respect to the crack geometry is required in order to determine the interpolation functions in X-FEM, the level set method (4) , which expresses the geometry implicitly as the zero contour of the level set function, can be used in order to simplify the computation process in X-FEM analysis (5) . The X-FEM analyses in conjunction with the level set method (6) have been applied to the three-dimensional elastic stress and crack propagation analyses for planar and non-planar crack with complex geometry (7) (8) . Moreover, X-FEM has come to be applied to geometrically nonlinear (9) (10) and materially nonlinear problems (10)-(13) . In elastic problems, the energy release rate, which is one of fracture mechanics parameters, can be evaluated by the post processing for the results of X-FEM analysis, as well as FEM. Since the crack geometry does not always perfectly coincide with the element boundary in X-FEM models, neither the virtual crack closure method (14) nor the virtual crack extension method (15) (16) can be applied directly. Therefore, the domain integral method (17) (18) is used to evaluate the Vol. 2, No. 1, 2008 211 energy release rate Journal of Computational Science and Technology(1)- (3), (6)- (8) .The symmetrical conditions can be considered in order to reduce the number of nodes and elements and perform effective analyses in X-FEM as well as FEM when the geometry and boundary conditions have the symmetry properties. However, because the interpolation functions utilized in X-FEM analyses include the enrichment basis functions a...

Simulation of Ductile Crack Propagation for Pipe Structures Using X-FEM

“…The X-FEM analysis considering symmetry conditions is detailed in Ref. (3). Figure 4 shows examples of finite element mesh for FEM and X-FEM analysis.…”

“…An innovative finite element analysis method, extended finite element method (X-FEM) (2) , is regarded as a promising numerical technique with high accuracy in consideration of the specific characteristic of the analysis objects. Applying the method to crack problems, efficient numerical analysis can be realized using finite element mesh that is independent of the existence or the extension of a crack (3,4) . The X-FEM analyses in conjuction with the level set method (5) have been applied to the three-dimensional elastic stress and crack propagation analyses for planar and non-planar crack with complex geometry (6,7) , however, they were intended for fatigue crack propagation only.…”