scholarly journals Correction force for releasing crack tip element with XFEM and only discontinuous enrichment

2009 ◽  
pp. 465-483
Author(s):  
Thomas Menouillard ◽  
Ted Belytschko
Keyword(s):  
Finite Element Method ◽  
Extended Finite Element Method ◽  
Crack Tip ◽  
Stress Waves ◽  
Intensity Factors ◽  
Extended Finite Element ◽  
Binary Description ◽  
Discontinuous Enrichment ◽  
Internal Forces ◽  
Crack Tip Element

This paper deals with numerical crack propagation and makes use of the extended finite element method in the case of explicit dynamics. The advantage of this method is the absence of remeshing. The use of XFEM with Heaviside functions only gives a binary description of the crack tip element: cut or not. Here, we modify the internal forces with a correction force in order to smoothly release the tip element while the virtual crack tip travels through an element. This avoids creating non physical stress waves and improves the accuracy of the evaluation of the stress intensity factors during propagation.

On XFEM Applications to Crack Surface under External Force

2012 ◽  
Vol 152-154 ◽  
pp. 210-215
Author(s):  
Tian Tang Yu ◽  
Lu Yang Shi
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Stress Intensity ◽  
Extended Finite Element Method ◽  
Crack Surface ◽  
Water Pressure ◽  
Intensity Factors ◽  
Extended Finite Element ◽  
Modeling Growth ◽  
Element Method

The extended finite element method is applied to modeling growth of arbitrary crack with crack surface tractions. Firstly, the extended finite element method is investigated for the stress intensity factor solution of surface traction problems. Secondly, for different water pressure acting on the crack surfaces and different crack length, the variation of the stress intensity factors is investigated. Finally, the process of hydraulic fracturing is simulated with the method. Numerical simulations illustrate that the method can effectively model the fracture problems with surface tractions.

scholarly journals The Numerical Simulation of the Crack Elastoplastic Extension Based on the Extended Finite Element Method

2013 ◽  
Vol 2013 ◽  
pp. 1-13
Author(s):  
Xia Xiaozhou ◽  
Zhang Qing ◽  
Wang Hong ◽  
Jiang Qun
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Basis Function ◽  
Extended Finite Element Method ◽  
Crack Tip ◽  
Function Form ◽  
Extended Finite Element ◽  
Polar Radius ◽  
Radius Function ◽  
Element Method

In the frame of the extended finite element method, the exponent disconnected function is introduced to reflect the discontinuous characteristic of crack and the crack tip enrichment function which is made of triangular basis function, and the linear polar radius function is adopted to describe the displacement field distribution of elastoplastic crack tip. Where, the linear polar radius function form is chosen to decrease the singularity characteristic induced by the plastic yield zone of crack tip, and the triangle basis function form is adopted to describe the displacement distribution character with the polar angle of crack tip. Based on the displacement model containing the above enrichment displacement function, the increment iterative form of elastoplastic extended finite element method is deduced by virtual work principle. For nonuniform hardening material such as concrete, in order to avoid the nonsymmetry characteristic of stiffness matrix induced by the non-associate flowing of plastic strain, the plastic flowing rule containing cross item based on the least energy dissipation principle is adopted. Finally, some numerical examples show that the elastoplastic X-FEM constructed in this paper is of validity.

scholarly journals CRACK INFLUENCE ON A PIPE WITH DOUBLE SLOPE UNDER INTERNAL PRESSURE: NUMERICAL SIMULATION WITH XFEM

2020 ◽  
Vol 21 (2) ◽  
pp. 266-283
Author(s):  
Houda Salmi ◽  
Abdelilah Hachim ◽  
Hanan El Bhilat ◽  
Khalid El Had
Keyword(s):  
Numerical Simulation ◽  
Finite Element Method ◽  
Stress Intensity ◽  
Stress Intensity Factors ◽  
Level Sets ◽  
Extended Finite Element Method ◽  
Three Dimensional ◽  
Intensity Factors ◽  
Extended Finite Element ◽  
Elliptical Cracks

This work analyses the effect of elliptical cracks on a pipe with double slope thickness transition, using the extended finite element method (XFEM), level sets were defined to describe the three-dimensional (3D) cracks. The Computation of the stress intensity factors (SIFs) of cracks is performed. The values of SIFs are compared between straight pipes and pipes with a double (single) slope thickness transition. The results show that the XFEM is an effective tool for modelling cracks in pipes. A pressurized pipe with double slope thickness transition is more sensitive to the defect in comparison with another type of pipe. Parameters of the transition zone have an effect on stress intensity factors, precisely, the parameters of the first thickness transition are more influential on the gravity of the defect compared to the second thickness transition. ABSTRAK: Kajian ini menganalisa kesan retakan elips pada paip dengan peralihan ketebalan cerun berganda, menggunakan kaedah elemen terhingga dipanjangkan (XFEM), set tahap ditentukan bagi menentukan keretakan tiga dimensi (3D). Pengiraan faktor intensiti tekanan (SIF) retakan dilakukan. Nilai SIF dibandingkan antara paip lurus dan paip peralihan ketebalan cerun berganda (tunggal). Hasil kajian menunjukkan bahawa XFEM adalah alat yang berkesan bagi memodel keretakan paip. Paip bertekanan mengikut peralihan ketebalan cerun berganda, lebih sensitif terhadap kecacatan berbanding paip lain. Parameter zon peralihan mempunyai pengaruh terhadap faktor intensiti tegangan, tepatnya, parameter peralihan ketebalan pertama lebih mempengaruhi pada graviti kecacatan berbanding dengan peralihan ketebalan kedua.

New anisotropic crack-tip enrichment functions for the extended finite element method

2012 ◽  
Vol 50 (5) ◽  
pp. 591-601 ◽  
Author(s):  
G. Hattori ◽  
R. Rojas-Díaz ◽  
A. Sáez ◽  
N. Sukumar ◽  
F. García-Sánchez
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Extended Finite Element Method ◽  
Crack Tip ◽  
Extended Finite Element ◽  
Element Method

scholarly journals Mechanical Behavior of Double-Arch Tunnels under the Effect of Voids on the Top of the Middle Wall

Symmetry ◽  
2018 ◽  
Vol 10 (12) ◽  
pp. 703 ◽  
Author(s):  
Bo Min ◽  
Xu Zhang ◽  
Chengping Zhang ◽  
Yanping Gong ◽  
Tengfei Yuan
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Mechanical Behavior ◽  
Extended Finite Element Method ◽  
Crack Depth ◽  
Void Size ◽  
Extended Finite Element ◽  
Two Factors ◽  
Internal Forces ◽  
And Performance

Voids behind linings may affect the safety and performance of structures. In this paper, the applicability of the extended finite element method for simulating crack propagation was verified firstly through comparisons between numerical simulations and model tests. Moreover, the mechanical behavior of double-arch tunnels under effects of voids on the top of the middle wall was investigated numerically. Two factors, including void size and tunnel shape, were mainly investigated. The main results obtained were explored including internal forces, deformation and fracturing of the liner. The results showed that voids produced adverse effects on the liner. Internal forces on the liner experienced significant changes and the deformation of the liner increased. Besides, larger crack depth was observed at the crown and the connection between the spandrel and middle wall, indicating a significant decrease in bearing capacity of the structure compared with tunnels without voids.

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