An extended finite element method scheme for sharp V-notches is developed. The method allows the representation of notch faces independent of the mesh. This is achieved by enriching the finite element approximation of the nodes surrounding the notch tip with the first term of the notch tip asymptotic field and the nodes that intersect the notch faces with a jump enrichment function using a partition of unity method. The least-squares method is used to evaluate the stress intensity factors of sharp V-notches. Numerical simulations demonstrate the accuracy and the robustness of the proposed technique.
NiuZRChengCZYeJQ. A new boundary element approach of modeling singular stress fields of plane V-notch problems. Int J Solids Structs2009; 46(16): 2999–3008.
LinKYTongP. Singular finite elements for the fracture analysis of V-notched plate. Int J Numer Methods Engng1980; 15(9): 1343–1354.
4.
JuSH. Finite element calculation of stress intensity factors for interface notches. Comput Methods Appl Mech Engng2010; 199(33-36): 2273–2280.
5.
GrossBMendelsonA. Plane elastostatic analysis of V-notched plates. Int J Fracture Mech1972; 8(3): 267–276.
6.
CarpenterWC. Calculation of fracture mechanics parameters for a general corner. Int J Fracture1984; 24(1): 45–48.
7.
ChenDH. Stress intensity factors for V-notched strip under tension or in-plane bending. Int J Fracture1995; 70(1): 81–97.
8.
NodaNAOdaKInoueT. Analysis of newly defined stress intensity factors for angular corners using singular integral equation of the body force method. Int J Fracture1995; 76(3): 243–261.
9.
NodaNATakaseY. Generalized stress intensity factors of V-shaped notch in a round bar under torsion, tension, and bending. Engng Fracture Mech2003; 70(11): 1447–1466.
10.
SewerynA. Modeling of singular stress fields using finite element method. Int J Solids Structs2002; 39(18): 4787–4804.
11.
ChangJHWuWH. Calculation of mixed-mode stress field at a sharp notch tip using M1ϵ-integral. Comput Mech2003; 31(5): 419–427.
12.
LiuYHWuZGLiangYC. Numerical methods for determination of stress intensity factors of singular stress field. Engng Fracture Mech2008; 75(16): 4793–4803.
13.
TreifiMOyadijiSOTsangDKL. Computation of the stress intensity factors of sharp notched plates by the fractal-like finite element method. Int J Numer Methods Engng2009; 77(4): 558–580.
14.
JuSHChungHY. Accuracy and limit of a least-squares method to calculate 3D notch SIFs. Int J Fracture2007; 148(2): 169–183.
15.
AyatollahiMRNejatiM. Determination of NSIFs and coefficients of higher order terms for sharp notches using finite element method. Int J Mech Sci2011; 53(3): 164–177.
16.
SzabóBAYosibashZ. Numerical analysis of singularities in two dimensions. Part 2: computation of generalized flux/stress intensity factors. Int J Numer Methods Engng1996; 39(3): 409–434.
17.
LabossierePEWDunnML. Stress intensities at interface corners in anisotropic biomaterials. Engng Fracture Mech1999; 62(6): 555–575.
18.
HwuCKuoTL. A unified definition for stress intensity factors of interface corners and cracks. Int J Solids Structs2007; 44(18-19): 6340–6359.
19.
QianZQ. On the evaluation of wedge corner stress intensity factors of bi-material joint with surface tractions. Comput Structs2001; 79(1): 53–64.
20.
SternMBeckerEBDunhamRS. A contour integral computation of mixed-mode stress intensity factors. Int J Fracture1976; 12(3): 359–368.
21.
BabuškaIMillerA. The post-processing approach in the finite element method—Part 1: calculation of displacements stresses and other higher derivatives of displacements. Int J Numer Methods Engng1984; 20(6): 1085–1109.
22.
BabuškaIMillerA. The post-processing approach in the finite element method—Part 2: calculation of the stress intensity factors. Int J Numer Methods Engng1984; 20(6): 1111–1129.
23.
BelytschkoTBlackT. Elastic crack growth in finite elements with minimal remeshing. Int J Numer Methods Engng1999; 45(5): 601–620.
24.
MoësNDolbowJBelytschkoT. A finite element method for crack growth without remeshing. Int J Numer Methods Engng1999; 46(1): 131–150.
25.
SukumarNMoësNMoranB. Extended finite element method for three-dimensional crack modeling. Int J Numer Methods Engng2000; 48(11): 1549–1570.
26.
XuYJYuangH. Computational modeling of mixed-mode fatigue crack growth using extended finite element methods. Int J Fracture2009; 159(2): 151–165.
27.
ElguedjTGravouilACombescureA. Appropriate extended functions for X-FEM simulation of plastic fracture mechanics. Comput Methods Appl Mech Engng2006; 195(7-8): 501–515.
28.
KarihalooBLXiaoQZ. Modelling of stationary and growing cracks in FE framework without remeshing: a state-of-the-art review. Comput Structs2003; 81(3): 119–129.
29.
RabczukTBordasSZiG. On three-dimensional modelling of crack growth using partition of unity methods. Comput Structs2010; 88(23-24): 1391–1411.
30.
YazidAAbdelkaderNAbdelmadjidH. A state-of-the-art review of the X-FEM for computational fracture mechanics. Appl Math Modelling2009; 33(12): 4269–4282.
31.
BrahtzJHA. Stress distribution in a reentrant corner. Trans Am Soc Mech Engrs1933; 55: 31–37.
32.
WilliamsML. Stress singularities resulting from various boundary conditions in angular corners of plates in extension. J Appl Mech1952; 19(4): 526–528.
33.
VasilopoulosD. On the determination of higher order terms singular elastic stress fields near corners. Numedsche Mathematik1988; 53(1-2): 51–59.
34.
AsadpoureAMohammadiS. Developing new enrichment functions for crack simulation in orthotropic media by the extended finite element method. Int J Numer Methods Engng2007; 69(10): 2150–2172.
35.
CoxJV. An extended finite element method with analytical enrichment for cohesive crack modeling. Int J Numer Methods Engng2009; 78(1): 48–84.
36.
GroßSReuskenA. An extended pressure finite element space for two-phase incompressible flows with surface tension. J Comput Phys2007; 224(1): 40–58.
37.
SukumarNChoppDLMoësN. Modeling holes and inclusions by level sets in the extended finite-element method. Comput Methods Appl Mech Engng2001; 190(46-47): 6183–6200.
38.
JuSH. Simulating three-dimensional stress intensity factors by the least-squares method. Int J Numer Method Engng1998; 43(8): 1437–1451.
39.
GrossB. Some plane problem elastostatic solutions for plates having a V-notch. PhD Thesis, CaseWestern Reserve University, 1970.
