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Journal articles on the topic 'Extended finite element method (XFEM)'

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Published: 4 June 2021
Last updated: 2 September 2023

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1

Li, Tingyu, Dongxu Han, Fusheng Yang, Bo Yu, Dongliang Sun, and Jinjia Wei. "A comparative study on simulating flow-induced fracture deformation in subsurface media by means of extended FEM and FVM." Oil & Gas Science and Technology – Revue d’IFP Energies nouvelles 75 (2020): 41. http://dx.doi.org/10.2516/ogst/2020037.

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Accurate and efficient simulation on the fluid flow and deformation in porous media is of increasing importance in a diverse range of engineering fields. At present, there are only several methods can be used to simulate the deformation of fractured porous media. It is very important to know their application scopes, advantages, and disadvantages for solving the practical problems correctly. Therefore, in this paper, we compared two numerical simulation methods for flow-induced fracture deformation in porous media. One is the Extended Finite Element Method (XFEM), which is based on the classical finite element method and can simulate strong or weak discontinuous problems. The other is developed within the finite-volume framework, termed Extended Finite Volume Method (XFVM). We designed three test cases, including single fracture, cross fractures and eight discrete fractures, to investigate the accuracy and efficiency of XFEM and XFVM. The reference solutions were provided by the commercial software, COMSOL, where the standard finite element method is implemented. The research findings showed that the accuracy of the XFEM was slightly higher than that of the XFVM, but the latter was more efficient. These results are likely to be useful in decision making regarding choice of solving methods for the multi-field coupling problem in fractured porous media.
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2

Wang, Feng, Di Zhang, Jing Yu, and Hui Xu. "Numerical Integration Technique in Computation of Extended Finite Element Method." Advanced Materials Research 446-449 (January 2012): 3557–60. http://dx.doi.org/10.4028/www.scientific.net/amr.446-449.3557.

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The extended finite element method (XFEM) is the most effective numerical method to solve discontinuous dynamic problems so far. It makes research within a standard finite element framework and reserves all merits of CFEM. In other side, it needs not mesh repartition to geometric and physical interface. Numerical integration techniques of the XFEM computation are studied, including displacement mode of the XFEM, control equation and infirm solution form of discontinuous medium mechanics problem, region scatteration, element integral strategy.
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3

Zhou, Li Ming, Guang Wei Meng, Feng Li, and Shuai Gu. "A Cell-Based Smoothed XFEM for Fracture in Piezoelectric Materials." Advances in Materials Science and Engineering 2016 (2016): 1–14. http://dx.doi.org/10.1155/2016/4125307.

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This paper presents a cell-based smoothed extended finite element method (CS-XFEM) to analyze fractures in piezoelectric materials. The method, which combines the cell-based smoothed finite element method (CS-FEM) and the extended finite element method (XFEM), shows advantages of both methods. The crack tip enrichment functions are specially derived to represent the characteristics of the displacement field and electric field around the crack tip in piezoelectric materials. With the help of the smoothing technique, integrating the singular derivatives of the crack tip enrichment functions is avoided by transforming interior integration into boundary integration. This is a significant advantage over XFEM. Numerical examples are presented to highlight the accuracy of the proposed CS-XFEM with the analytical solutions and the XFEM results.
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4

Zhang, Di, Feng Wang, and Hui Xu. "Study of Numerical Problem Based on the Extended Finite Element Method." Advanced Materials Research 472-475 (February 2012): 1623–26. http://dx.doi.org/10.4028/www.scientific.net/amr.472-475.1623.

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The extended finite element method (XFEM) provides an effective tool for analyzing crack problems.The control equations and the weak form can be established through balance equations ,boundary condition, geometry equations,etc.After the establishment of stiffness matrix,the crack problems can be solved by XFEM conveniently.
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5

Tang, Yu Xiang, and Hong Niao Chen. "Simulation of Crack Propagation in Concrete Based on Extended Finite Element Method." Key Engineering Materials 783 (October 2018): 165–69. http://dx.doi.org/10.4028/www.scientific.net/kem.783.165.

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Fracture behaviors in concrete beam subjected to three-point bending was numerically simulated using extended finite element method (XFEM). The entire load-displacement curves and crack path obtained by numerical simulation were compared with that measured from experimental tests. Compared with the experimental results, the errors of numerical Pc and δc were smaller than 10% and the error of CMODc was lower than 2%, verifying the validity and accuracy of XFEM model. Whether a XFEM simulation or a test, the propagation direction of the main crack is toward to the upper loading point. At the peak load, the crack lengths measured by ESPI and XFEM were 93 μm and 97 μm respectively.
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6

Duan, Nana, Shaocong Lu, Xinyu Ma, Weijie Xu, Fuquan Jin, and Shuhong Wang. "Research on Extended Finite Element Method for Axisymmetric Electrostatic Field Based on Liquid Nitrogen with Bubbles." Applied Sciences 11, no. 11 (June 4, 2021): 5214. http://dx.doi.org/10.3390/app11115214.

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In this paper, the extended finite element method (XFEM) is first applied to account for the weak discontinuity of the axisymmetric electrostatic field. Firstly, the interface between two materials in an element is described by the level set method. The enrichment function is used to modify the shape function of enrichment elements. Secondly, to illustrate the feature of the enrichment function, the distribution diagrams of enrichment functions in sub-elements are drawn. The 3D field can be simplified to an axisymmetric field, which can reduce the difficulty of calculation. Finally, models with bubbles in liquid nitrogen in the axisymmetric field are used to prove the reliability of XFEM. Compared with the conventional finite element method (CFEM), XFEM costs lower computing resources with almost the same computational accuracy.
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7

Yan, Ke Bin, Zheng Xiang Huang, Rong Zhong Liu, and Feng Wang. "Research of the Penetration Process for Concrete Target Based on the Extended Finite Element Method." Applied Mechanics and Materials 644-650 (September 2014): 429–32. http://dx.doi.org/10.4028/www.scientific.net/amm.644-650.429.

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The extended finite element method (XFEM) is the most effective numerical method to solve discontinuous dynamic problems so far. It makes research within a standard finite element framework and needs not mesh repartition to geometric and physical interface, so it reserves all merits of the conventional finite element method (CFEM). The XFEM was applied to the penetration process for concrete target in the paper, and the displacement mode of elements with cracks and fracture criterion were presented. Then the weak solutions of control equations were discretized in different areas. The numerical examples for steel rod penetrating in the concrete target concluded that the method and program were reasonable and effective. The effect discipline of crack growth to the concrete material penetration process was summarized, and it would establish theoretic base for the further application of the XFEM.
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8

Yu, Miao, Zhi Hong Dai, and Gui Juan Hu. "Crack Extension Calculation under Tensile and Shear Load by XFEM." Applied Mechanics and Materials 580-583 (July 2014): 3046–50. http://dx.doi.org/10.4028/www.scientific.net/amm.580-583.3046.

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The extended finite element method (XFEM) is a numerical method for modeling discontinuity such as cracks, holes, inclusions etc within a standard finite element framework. In the XFEM, special functions which can reflect the problem’s solution characteristics are added to the finite element approximation using the framework of partition of unity. Compared with the standard finite element method, it obtained more accuracy without remeshing. In this paper, we studied crack propagation behavior under different proportions of tension and shear loads by XFEM.
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9

Jiang, Youshi, Jinzhou Zhao, Yongming Li, Hu Jia, and Liehui Zhang. "Extended Finite Element Method for Predicting Productivity of Multifractured Horizontal Wells." Mathematical Problems in Engineering 2014 (2014): 1–9. http://dx.doi.org/10.1155/2014/810493.

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Based on the theory of the extended finite element method (XFEM), which was first proposed by Moës for dealing with the problem characterized by discontinuities, an extended finite element model for predicting productivity of multifractured horizontal well has been established. The model couples four main porous flow regimes, including fluid flow in the away-from-wellbore region of reservoir matrix, radial flow in the near-wellbore region of reservoir matrix, linear flow in the away-from-wellbore region of fracture, and radial flow in the near-wellbore region of fracture by considering mass transfer between fracture and matrix. The method to introduce the interior well boundary condition into the XFEM is proposed, and therefore the model can be highly adaptable to the complex and asymmetrical physical conditions. Case studies indicate that this kind of multiflow problems can be solved with high accuracy by the use of the XFEM.
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10

Doškář, Martin, Jan Novák, and Jan Zeman. "Wang Tiling Based Enrichment Functions for Extended Finite Element Method." Advanced Materials Research 1144 (March 2017): 102–8. http://dx.doi.org/10.4028/www.scientific.net/amr.1144.102.

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The Extended Finite Element Method (XFEM) enhances the approximation space of the standard Finite Element Method (FEM) with functions reflecting local features in order to yield more accurate results with less degrees of freedom. XFEM performance is, thus, closely related to the quality of enrichment functions. Analogously to our previous works, in which we have employed the concept of Wang tiles to assembly microstructure geometries, in this contribution we use Wang tiles to assemble microstructure-informed enrichment functions. We compare two ways of generating the enrichments: (i) inspired by the first-order numerical homogenization and (ii) based on spectral analysis of the global stiffness matrix for the whole set. The methodology and performance of both approaches are illustrated through a linear diffusion problem in two dimensions
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11

Li, Wei, Huangjian Yi, Qitan Zhang, Duofang Chen, and Jimin Liang. "Extended Finite Element Method with Simplified Spherical Harmonics Approximation for the Forward Model of Optical Molecular Imaging." Computational and Mathematical Methods in Medicine 2012 (2012): 1–10. http://dx.doi.org/10.1155/2012/394374.

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An extended finite element method (XFEM) for the forward model of 3D optical molecular imaging is developed with simplified spherical harmonics approximation (SPN). In XFEM scheme ofSPNequations, the signed distance function is employed to accurately represent the internal tissue boundary, and then it is used to construct the enriched basis function of the finite element scheme. Therefore, the finite element calculation can be carried out without the time-consuming internal boundary mesh generation. Moreover, the required overly fine mesh conforming to the complex tissue boundary which leads to excess time cost can be avoided. XFEM conveniences its application to tissues with complex internal structure and improves the computational efficiency. Phantom and digital mouse experiments were carried out to validate the efficiency of the proposed method. Compared with standard finite element method and classical Monte Carlo (MC) method, the validation results show the merits and potential of the XFEM for optical imaging.
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12

Chen, Xinya, Zhen Chen, and Yang Zhao. "Analysis of Sheet Fracture Failure Based on XFEM." Open Mechanical Engineering Journal 9, no. 1 (October 7, 2015): 887–91. http://dx.doi.org/10.2174/1874155x01509010887.

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Extended finite element method (XFEM) is the most effective numerical method to solve discrete mechanical problem. Crack growth problem of two-dimension finite length rectangle panel is researched based on Abaqus XFEM frame. Stress intensity factor is obtained respectively by theoretical calculation and XFEM simulation, which proves reliability of XFEM and the software.
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13

Bobiński, J., and J. Tejchman. "Application of Extended Finite Element Method to Cracked Concrete Elements – Numerical Aspects." Archives of Civil Engineering 58, no. 4 (December 1, 2012): 409–31. http://dx.doi.org/10.2478/v.10169-012-0022-z.

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AbstractThe paper deals with the application of the eXtended Finite Element Method (XFEM) to simulations of discrete macro-cracks in plain concrete specimens under tension, bending and shear. Fundamental relationships and basic discrete constitutive laws were described. The most important aspects of the numerical implementation were discussed. Advantages and disadvantages of the method were outlined
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14

Chessa, Jack, Patrick Smolinski, and Ted Belytschko. "The extended finite element method (XFEM) for solidification problems." International Journal for Numerical Methods in Engineering 53, no. 8 (2002): 1959–77. http://dx.doi.org/10.1002/nme.386.

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15

Malekan, Mohammad, Felício Barros, Roque Luiz da Silva Pitangueira, Phillipe Daniel Alves, and Samuel Silva Penna. "A computational framework for a two-scale generalized/extended finite element method." Engineering Computations 34, no. 3 (May 2, 2017): 988–1019. http://dx.doi.org/10.1108/ec-02-2016-0050.

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Purpose This paper aims to present a computational framework to generate numeric enrichment functions for two-dimensional problems dealing with single/multiple local phenomenon/phenomena. The two-scale generalized/extended finite element method (G/XFEM) approach used here is based on the solution decomposition, having global- and local-scale components. This strategy allows the use of a coarse mesh even when the problem produces complex local phenomena. For this purpose, local problems can be defined where these local phenomena are observed and are solved separately by using fine meshes. The results of the local problems are used to enrich the global one improving the approximate solution. Design/methodology/approach The implementation of the two-scale G/XFEM formulation follows the object-oriented approach presented by the authors in a previous work, where it is possible to combine different kinds of elements and analyses models with the partition of unity enrichment scheme. Beside the extension of the G/XFEM implementation to enclose the global–local strategy, the imposition of different boundary conditions is also generalized. Findings The generalization done for boundary conditions is very important, as the global–local approach relies on the boundary information transferring process between the two scales of the analysis. The flexibility for the numerical analysis of the proposed framework is illustrated by several examples. Different analysis models, element formulations and enrichment functions are used, and the accuracy, robustness and computational efficiency are demonstrated. Originality/value This work shows a generalize imposition of different boundary conditions for global–local G/XFEM analysis through an object-oriented implementation. This generalization is very important, as the global–local approach relies on the boundary information transferring process between the two scales of the analysis. Also, solving multiple local problems simultaneously and solving plate problems using global–local G/XFEM are other contributions of this work.
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16

Su, Yi, Sheng Nan Wang, and Yong En Du. "Optimization Algorithm of Crack Initial Angle Using the Extended Finite Element Method." Applied Mechanics and Materials 444-445 (October 2013): 77–84. http://dx.doi.org/10.4028/www.scientific.net/amm.444-445.77.

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The extended finite element method (XFEM) allows the entire crack to be represented independently from the mesh, which means re-mesh is unnecessary in model crack growth, reduces the computational time drastically. However, fatigue crack growth simulation has been computationally challenged by lots of analog computations in crack growth. Therefore, a new reanalysis algorithm based on incremental Cholesky factorization is derived. In this paper, we consider a variant of XFEM in which an exponent discontinuous function is used to simulate the crack through unit. Then the corresponding formula of XFEM with inclusion and crack problem with a new reanalysis algorithm is derived. In the end, we use the new reanalysis algorithm and an optimization algorithm to predict the angle of crack initiation from a hole in a plate with inclusion. It shows that the algorithm is effective.
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17

Li, Lin Sheng, Chang Jun Qiu, and Lan Li. "An Integration Scheme of Extended Finite Element Method." Applied Mechanics and Materials 148-149 (December 2011): 286–90. http://dx.doi.org/10.4028/www.scientific.net/amm.148-149.286.

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A simple integration scheme is presented for numerical integration in the extended finite element method(XFEM). In this scheme, the integral domain of common triangular mesh is converted to that of standard triangular mesh and the integral domain of standard triangular mesh is converted to that of quadrilateral mesh. By this transformation of integral domain, the strength intensity factors for straight crack are worked out. Finally, the accuracy of this method is analyzed by a typical example. It is concluded that the results obtained by new integral scheme are more accurate and simple than common Gaussian integration scheme.
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18

Song, Jeong-Hoon, Patrick Lea, and Jay Oswald. "Explicit Dynamic Finite Element Method for Predicting Implosion/Explosion Induced Failure of Shell Structures." Mathematical Problems in Engineering 2013 (2013): 1–11. http://dx.doi.org/10.1155/2013/957286.

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A simplified implementation of the conventional extended finite element method (XFEM) for dynamic fracture in thin shells is presented. Though this implementation uses the same linear combination of the conventional XFEM, it allows for considerable simplifications of the discontinuous displacement and velocity fields in shell finite elements. The proposed method is implemented for the discrete Kirchhoff triangular (DKT) shell element, which is one of the most popular shell elements in engineering analysis. Numerical examples for dynamic failure of shells under impulsive loads including implosion and explosion are presented to demonstrate the effectiveness and robustness of the method.
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19

Jiang, Yong, and Eric Li. "XFEM with Smoothing Technique for Static Fracture Mechanics in Three-Dimension." International Journal of Computational Methods 13, no. 02 (March 2016): 1640004. http://dx.doi.org/10.1142/s0219876216400041.

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In this work, the advantages of face-based smoothing technique and extended finite element method (XFEM) are combined to develop a face-based smoothed extended finite element method (FS-XFEM). By this new method, arbitrary crack geometry can be modeled and crack advance can be simulated without remeshing. At the same time, the integration of singular term over the volume around the crack front can be eliminated induced by the transformation of volume integration into area integration. Numerical examples are presented to test the accuracy and convergence rate of the FS-XFEM. From the results, it is clear that smoothing technique can improve the performance of XFEM for three-dimensional fracture problems.
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20

CHEN, L., G. R. LIU, and K. Y. ZENG. "A COMBINED EXTENDED AND EDGE-BASED SMOOTHED FINITE ELEMENT METHOD (ES-XFEM) FOR FRACTURE ANALYSIS OF 2D ELASTICITY." International Journal of Computational Methods 08, no. 04 (November 20, 2011): 773–86. http://dx.doi.org/10.1142/s0219876211002812.

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This study combines the edge-based smoothed finite element method (ES-FEM) and the extended finite element method (XFEM) to develop a new simulation technique (ES-XFEM) for fracture analysis of 2D elasticity. In the XFEM, the need for the mesh alignment with the crack and remeshing, as the crack evolves, is eliminated because of the use of partition of unity. The ES-FEM uses the generalized smoothing operation over smoothing domain associated with edges of simplex meshes, and produces a softening effect leading to a close-to-exact stiffness, "super-convergence" and "ultra-accurate" solutions for the numerical model. Taking advantage of both ES-FEM and XFEM, the present method introduces the edge-based strain smoothing technique into the context of XFEM. Thanks to strain smoothing, the necessity of sub-division in elements cut by discontinuities is suppressed via transforming interior integration into boundary integration. Hence, it simplifies the numerical integration procedure in the XFEM. Numerical examples showed that the proposed method improves significantly the accuracy of stress intensity factors and achieves a quasi optimal convergence rate in the energy norm without geometrical enrichment or blending correction.
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21

Abdi, M., I. Ashcroft, and R. D. Wildman. "Topology Optimization of Geometrically Non-Linear Structures Using Iso-XFEM Method." Key Engineering Materials 627 (September 2014): 121–24. http://dx.doi.org/10.4028/www.scientific.net/kem.627.121.

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Iso-XFEM is an evolutionary-based topology optimization method which couples the extended finite element method (X-FEM) with an isoline/isosurface optimization approach, enabling a smooth and accurate representation of the design boundary in a fixed-grid finite element mesh. This paper investigates the application of the Iso-XFEM method to the topology optimization of structures which experience large deformation. The total Lagrangian formulation of the finite element method is employed to model the geometrically non-linear behaviour and equilibrium is found by implementing the Newton-Raphson method in each evolution. A cantilever beam is considered as a test case and the Iso-XFEM solutions obtained from linear and non-linear designs are compared with bi-directional evolutionary structural optimization (BESO) solutions.
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22

Cen, Yi. "Extended Finite Element Method for Fracture Mechanics and Mesh Refinement Controlled by Density Function." Key Engineering Materials 525-526 (November 2012): 413–16. http://dx.doi.org/10.4028/www.scientific.net/kem.525-526.413.

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This paper discusses the combination of element enrichment by mesh refinement controlled by density function with the extended finite element method and its application in fracture mechanics. Extended finite element method (XFEM) is an effective numerical method for solving discontinuity problems in the finite element work frame. A numerical example of fracture mechanics is analyzed at the end of this paper to show the application of the above method.
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23

Yu, T. T. "The extended finite element method (XFEM) for discontinuous rock masses." Engineering Computations 28, no. 3 (April 5, 2011): 340–69. http://dx.doi.org/10.1108/02644401111118178.

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24

Wang, Feng, Hui Xu, Jing Yu, Xi Quan Jiang, and Long Yu. "Application of the Extended Finite Element Method to the Penetration Problem for a Body with Cracks." Applied Mechanics and Materials 321-324 (June 2013): 146–49. http://dx.doi.org/10.4028/www.scientific.net/amm.321-324.146.

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The XFEM makes research within a standard finite element framework and needs not mesh repartition to geometric and physical interface, and it reserves all merits of the CFEM, therefore it is the most effective numerical method to solve discontinuous dynamic problems so far. The crack growth problem was studied in the XFEM computation, and the displacement mode of elements with cracks and fracture criterion were presented. The numerical examples for steel rod penetrating in the aluminum target concluded that the method and program were reasonable and effective. The crack growth discipline of penetration process for metal material was summarized, and it would establish theoretic base for the further application of the XFEM.
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LIU, S. "XRPIM versus XFEM." International Journal of Computational Methods 10, no. 01 (February 2013): 1340006. http://dx.doi.org/10.1142/s0219876213400069.

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We present an extended radial point interpolation method (XRPIM) for modeling cracks and material interfaces in two-dimensional elasto-static problems. Therefore, partition of unity enrichment is incorporated into RPIM. We employ both step enrichment and crack tip enrichment for cracks. The studies are restricted to stationary cracks though the method can be extended easily to moving boundaries. We compare the results to the extended finite element method to show the superiority of our method. We show for two selected problems that the error is of magnitudes lower compared to XFEM simulations.
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Qu, Hong Chang, Xiao Zhou Xia, and Zhi Qiang Xiong. "Numerical Simulation of Quasi-Brittle Fracture in Concrete Structures with Extended Finite Element Method." Advanced Materials Research 163-167 (December 2010): 1837–43. http://dx.doi.org/10.4028/www.scientific.net/amr.163-167.1837.

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In this paper, the extended finite element method (XFEM) is used for a discrete crack simulation of concrete using an adaptive crack growth algorithm. An interface model is proposed which includes normal and tangential displacements and allows the transfer of shear stresses through the interface. Different criteria for predicting the direction of the extension of a cohesive crack are conducted in the framework of the XFEM. On the basis of two examples, a comparison between the maximum circumferential stress criterion, the maximum energy release rate and the minimum potential energy criterion with experimental data has been carried out. The considered numerical simulations have confirmed the flexibility and effectiveness of the XFEM for the modelling of crack growth under general mode I and mixed-mode loading conditions.
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Jia, Honggang, Yufeng Nie, and Junlin Li. "Fracture Analysis in Orthotropic Thermoelasticity Using Extended Finite Element Method." Advances in Applied Mathematics and Mechanics 7, no. 6 (September 9, 2015): 780–95. http://dx.doi.org/10.4208/aamm.2014.m627.

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AbstractIn this paper, a method for extracting stress intensity factors (SIFs) in orthotropic thermoelasticity fracture by the extended finite element method (XFEM) and interaction integral method is present. The proposed method is utilized in linear elastic crack problems. The numerical results of the SIFs are presented and compared with those obtained using boundary element method (BEM). The good accordance among these two methods proves the applicability of the proposed approach and conforms its capability of efficiently extracting thermoelasticity fracture parameters in orthotropic material.
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Zhang, Hui Hua, and Dong Feng Zhou. "Extended Finite Element Analysis of Crack-Void Interaction Problems in Viscoelastic Materials." Applied Mechanics and Materials 353-356 (August 2013): 3186–89. http://dx.doi.org/10.4028/www.scientific.net/amm.353-356.3186.

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Due to the incorporation of enrichment functions in the displacement approximation, the mesh in the extended finite element method (XFEM) can be independent of the internal discontinuities. In the present paper, crack-void interaction problems in viscoelastic materials are investigated with the XFEM. The effect of the distance between crack and void on crack opening displacement is mainly studied in time domain.
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AN, XINMEI, GUOYANG FU, and GUOWEI MA. "A COMPARISON BETWEEN THE NMM AND THE XFEM IN DISCONTINUITY MODELING." International Journal of Computational Methods 09, no. 02 (June 2012): 1240030. http://dx.doi.org/10.1142/s0219876212400300.

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Discontinuities such as voids, cracks, material interfaces, and joints widely exist in nature. Conventional finite element method (FEM) requires the finite element mesh to coincide with the discontinuities, which often complicates the meshing task. When evolution of discontinuities are necessary, remeshing is inevitable, which makes the simulation tedious and time-consuming. In order to overcome such inconveniences, the extended finite element method (XFEM) and the generalized finite element method (GFEM) were developed by incorporating special functions into the standard finite element approximation space based on partition of unity. The finite element mesh is allowed to be totally independent of the discontinuities and remeshing is totally avoided for discontinuity evolution. The numerical manifold method (NMM) can also be viewed as an extension or generalization to the conventional FEM. Different from the XFEM/GFEM, the approximation in the NMM is based on covers. The NMM models discontinuities by its dual cover system. In this paper, a detailed comparison between the NMM and the XFEM in discontinuity modeling is presented. Their advantages and disadvantages are pointed out. How the dual cover system in the NMM favors the complex crack modeling is emphasized. Potential extensions to the XFEM and the NMM are suggested.
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30

Sarkar, Subhasis, Nicole Apetre, Nagaraja Iyyer, Nam Phan, Kishan Goel, and Satya Atluri. "Comparison of SGBEM-FEM Alternating Method and XFEM Method for Determining Stress Intensity Factor for 2D Crack Problems." Advanced Materials Research 891-892 (March 2014): 345–50. http://dx.doi.org/10.4028/www.scientific.net/amr.891-892.345.

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The two most promising approaches to determine Stress Intensity Factor (SIF) developedover the past decade are the Symmetric Galerkin Boundary Element Method - Finite Element Method(SGBEM-FEM) based alternating method and the Extended Finite Element (XFEM) method. Thepurpose of this paper is to determine the SIFs for a number of 2-D crack problems by the two ap-proaches and measure their relative effectiveness in terms of accuracy, speed and computational re-sources.In the SGBEM-FEM alternating method, a finite element analysis is carried out on the un-crackedbody using the externally applied loading and next a boundary element analysis is performed byreversing the stresses found on the crack location from the finite element analysis, and the residualstresses on the boundary of the finite body are determined. The steps are repeated until convergenceis achieved where the residual stresses on the boundaries and traction on the crack surfaces are closeto zero.In the XFEM method, the mesh is created without considering the topology of the crack configura-tion and the discontinuities are handled by special discontinuity enrichment functions. The enrichmentfunctions increase the degrees of freedom and the regular stiffness matrix is augmented by additionalterms corresponding to the extra degrees of freedom but the increase in computational requirement isoffset by not having the burden of remeshing the finite elements.Both SGBEM-FEM alternating method and XFEM method are used to solve a number of crackproblems and the example cases clearly show the computational efficiency of the SGBEM-FEM al-ternating method over the XFEM method.
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31

Lee, Sung-Jun, Sang-Hwan Lee, and Yoon-Suk Chang. "PWSCC Assessment by Using Extended Finite Element Method." Journal of Multiscale Modelling 06, no. 03 (September 2015): 1550007. http://dx.doi.org/10.1142/s1756973715500079.

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The head penetration nozzle of control rod driving mechanism (CRDM) is known to be susceptible to primary water stress corrosion cracking (PWSCC) due to the welding-induced residual stress. Especially, the J-groove dissimilar metal weld regions have received many attentions in the previous studies. However, even though several advanced techniques such as weight function and finite element alternating methods have been introduced to predict the occurrence of PWSCC, there are still difficulties in respect of applicability and efficiency. In this study, the extended finite element method (XFEM), which allows convenient crack element modeling by enriching degree of freedom (DOF) with special displacement function, was employed to evaluate structural integrity of the CRDM head penetration nozzle. The resulting stress intensity factors of surface cracks were verified for the reliability of proposed method through the comparison with those suggested in the American Society of Mechanical Engineering (ASME) code. The detailed results from the FE analyses are fully discussed in the manuscript.
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Giang, Nguyen Truong. "Numerical simulation of the crack 2D by the finite element incorporated the discontinuity." Vietnam Journal of Mechanics 30, no. 2 (July 1, 2008): 80–88. http://dx.doi.org/10.15625/0866-7136/30/2/5620.

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Determining stress intensity factors is important in fracture mechanics. The extended finite element method (XFEM) provides a robust and accurate to determine factors. This paper describes some results from the analysis of cracked plates using XFEM. Extended finite elements allow the entire crack to be represented independently of the meshing. The elements employ discontinuous functions and the facture mechanics two dimensional asymptotic crack tip displacement fields. The Fortran source code of Cast3M applies these elements to a set of examples. The obtained stress and deformation fields are used to compute stress intensity factors via interaction integrals. The results are compared with these obtained from conventional FEM to demonstrate the advantages of the employing the new elements.
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Zeller, Christian, Binu Surendran, and Micheal F. Zaeh. "Parameterized Extended Finite Element Method for high thermal gradients." Journal of Computational Design and Engineering 5, no. 3 (December 7, 2017): 329–36. http://dx.doi.org/10.1016/j.jcde.2017.12.001.

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Abstract The Finite Element Method results in inaccuracies for temperature changes at the boundary if the mesh is too coarse in comparison with the applied time step. Oscillations occur as the adjacent elements balance the excessive energy of the boundary element. An Extended Finite Element Method (XFEM) with extrinsic enrichment of the boundary element by a parameterized problem-specific ansatz function is presented. The method is able to represent high thermal gradients at the boundary with a coarse mesh as the enrichment function compensates for the excessive energy at the element affected by the temperature change. The parameterization covers the temporal change of the gradient and avoids the enrichment by further ansatz functions. The introduced parameterization variable is handed over to the system of equations as an additional degree of freedom. Analytical integration is used for the evaluation of the integrals in the weak formulation as the ansatz function depends non-linearly on the parameterization variable. Highlights Parameterized problem-specific ansatz functions. Avoidance of a fine mesh in the area of high gradients. Representation of high gradients with one additional DOF.
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Taj, Ali I., and Alaa H. Al-Zuhairi. "Behavior of Plain Concrete Beam Analyzed Using Extended Finite Element Method." Association of Arab Universities Journal of Engineering Sciences 26, no. 1 (March 31, 2019): 121–28. http://dx.doi.org/10.33261/jaaru.2019.26.1.016.

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In this study, plain concrete simply supported beams subjected to two points loading were analyzed for the flexure. The numerical model of the beam was constructed in the meso-scale representation of concrete as a two phasic material (aggregate, and mortar). The fracture process of the concrete beams under loading was investigated in the laboratory as well as by the numerical models. The Extended Finite Element Method (XFEM) was employed for the treatment of the discontinuities that appeared during the fracture process in concrete. Finite element method with the feature standard/explicitlywas utilized for the numerical analysis. Aggregate particles were assumedof elliptic shape. Other properties such as grading and sizes of the aggregate particles were taken from standard laboratory tests that conducted on aggregate samples.Two different concrete beamswere experimentally and numerically investigated. The difference between beams was concentrated in the maximum size of aggregate particles. The comparison between experimental and numerical results showed that themeso-scale model gives a good interface for the representing the concrete models in numerical approach. It was concluded that the XFEM is a powerful technique to use for the analysis of the fracture process and crack propagation in concrete.
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Pang, Yi Ling, and Duan Ming Dai. "XFEM for Crack Propagation in Fiber-Reinforced Materials." Advanced Materials Research 997 (August 2014): 450–53. http://dx.doi.org/10.4028/www.scientific.net/amr.997.450.

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This article describes the basic format of extended finite element method (XFEM), and simulation the crack propagation of fiber reinforced materials with extended finite element. Explore the number and elastic modulus of fibers influence the crack propagation by changing the elastic modulus and quantity of the fibers in matrix.
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Doškář, Martin, Jan Novák, and Jan Zeman. "SYNTHESIZED ENRICHMENT FUNCTIONS FOR EXTENDED FINITE ELEMENT ANALYSES WITH FULLY RESOLVED MICROSTRUCTURE." Acta Polytechnica CTU Proceedings 13 (November 13, 2017): 29. http://dx.doi.org/10.14311/app.2017.13.0029.

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Inspired by the first order numerical homogenization, we present a method for extracting continuous fluctuation fields from the Wang tile based compression of a material microstructure. The fluctuation fields are then used as enrichment basis in Extended Finite Element Method (XFEM) to reduce number of unknowns in problems with fully resolved microstructural geometry synthesized by means of the tiling concept. In addition, the XFEM basis functions are taken as reduced modes of a detailed discretization in order to circumvent the need for non-standard numerical quadratures. The methodology is illustrated with a scalar steady-state problem.
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Vu, Hoa Cong, and Dat Cong Nguyen. "APPLYING OF EXTENDED FINITE ELEMENT METHOD FOR CALCULATING STRESS INTENSITY FACTOR." Science and Technology Development Journal 13, no. 4 (December 30, 2010): 51–63. http://dx.doi.org/10.32508/stdj.v13i4.2168.

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Finite element method is a very powerful numerical method to predict and model mechanical behavior of material and structure. However, in some cases finite element method is more complicated like the modeling of moving discontinuities, hence the need to update the mesh to match the geometry of discontinuity. Extended finite element method (XFEM) allows us a new technique to modeling crack independently of the mesh; hence it is no need to remesh during propagation of the crack. In this paper, an extended finite element method is used to calculate stress intensity factor. It’s important parameter when we predict the direction of crack in the event of crack stops propagation.
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Campilho, Raul D. S. G., Arnaldo M. G. Pinto, Mariana D. Banea, Filipe J. P. Chaves, and Lucas F. M. da Silva. "Feasibility of the Extended Finite Element Method for the Simulation of Composite Bonded Joints." Materials Science Forum 730-732 (November 2012): 513–18. http://dx.doi.org/10.4028/www.scientific.net/msf.730-732.513.

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Adhesive-bonding for the unions in multi-component structures is gaining momentum over welding, riveting and fastening. It is vital for the design of bonded structures the availability of accurate damage models, to minimize design costs and time to market. Cohesive Zone Models (CZM’s) have been used for fracture prediction in structures. The eXtended Finite Element Method (XFEM) is a recent improvement of the Finite Element Method (FEM) that relies on traction-separation laws similar to those of CZM’s but it allows the growth of discontinuities within bulk solids along an arbitrary path, by enriching degrees of freedom. This work proposes and validates a damage law to model crack propagation in a thin layer of a structural epoxy adhesive using the XFEM. The fracture toughness in pure mode I (GIc) and tensile cohesive strength (sn0) were defined by Double-Cantilever Beam (DCB) and bulk tensile tests, respectively, which permitted to build the damage law. The XFEM simulations of the DCB tests accurately matched the experimental load-displacement (P-d) curves, which validated the analysis procedure.
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Lu, Wen Yan. "Failure Simulation of Single-Edge Notched Concrete Beam under Dynamic Tensile Loading." Applied Mechanics and Materials 638-640 (September 2014): 333–37. http://dx.doi.org/10.4028/www.scientific.net/amm.638-640.333.

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Crack growth of concrete beam under dynamic tensile loading is a typical discontinuous problem. It is difficult to realize the process of crack propagation using the conventional finite element method, but the extended finite element method (XFEM) is an effective method to analyze the fracture developed in recent years. This paper introduces the basic principle of XFEM and the analysis method of simulating concrete cracking and crack propagation with XFEM. At the end the crack expansion process of the concrete specimen with initial crack and dynamic load is done. The influence of crack propagation on concrete beam stresses and displacements and the crack propagation laws under dynamic tension is studied. The case shows the unique advantage of XFEM in the crack propagation analysis field.
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Taghezout, Ali, Bendouba Mostefa, Abdelkader Djebli, Aid Abdelkarim, and Habib Khellafi. "Experimental and Numerical Fracture Modeling Using XFEM of Aluminum Plates." International Journal of Engineering Research in Africa 46 (January 2020): 45–52. http://dx.doi.org/10.4028/www.scientific.net/jera.46.45.

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In this paper a numerical modeling was carried out to study the problem of plane elasticity in a medium cracked by the method of the extended finite elements (XFEM) in a thin cracked plate made of aluminum using the software Abaqus 6.13.This method improved the capability of the classical finite element method especially the crack propagation problems. Furthermore, the extended finite elements method has been used to simulate tensile and fracture behavior of the study materials. Based on variation in size and shape of crack, the results obtained will be compared with those obtained experimentally, this comparison shows a good agreement.
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Du, Quanshangze, Aline Bel-Brunon, Simon Auguste Lambert, and Nahiène Hamila. "Numerical simulation of wave propagation through interfaces using the extended finite element method for magnetic resonance elastography." Journal of the Acoustical Society of America 151, no. 5 (May 2022): 3481–95. http://dx.doi.org/10.1121/10.0011392.

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Magnetic resonance elastography (MRE) is an elasticity imaging technique for quantitatively assessing the stiffness of human tissues. In MRE, finite element method (FEM) is widely used for modeling wave propagation and stiffness reconstruction. However, in front of inclusions with complex interfaces, FEM can become burdensome in terms of the model partition and computationally expensive. In this work, we implement a formulation of FEM, known as the eXtended finite element method (XFEM), which is a method used for modeling discontinuity like crack and heterogeneity. Using a level-set method, it makes the interface independent of the mesh, thus relieving the meshing efforts. We investigate this method in two studies: wave propagation across an oblique linear interface and stiffness reconstruction of a random-shape inclusion. In the first study, numerical results by XFEM and FEM models revealing the wave conversion rules at linear interface are presented and successfully compared to the theoretical predictions. The second study, investigated in a pseudo-practical application, demonstrates further the applicability of XFEM in MRE and the convenience, accuracy, and speed of XFEM with respect to FEM. XFEM can be regarded as a promising alternative to FEM for inclusion modeling in MRE.
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42

Lateef, Hanadi, Rafil Laftah, and Nabeel Jasim. "Study on the Shear Failure of Reinforced Concrete Beams Using Extended Finite Element Method (XFEM)." Basrah journal for engineering science 21, no. 3 (October 5, 2021): 55–65. http://dx.doi.org/10.33971/bjes.21.3.7.

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This research concerns with the fracture behavior of reinforced concrete beams without shear reinforcement numerically. The software ABAQUS is adapted to simulate the crack propagation using the eXtended Finite Element Method (XFEM), taking into account materials nonlinearities using concrete damage plasticity CDP criteria. XFEM is used to solve the discontinuity problems in the simulation. The maximum principal stress failure criterion is selected for damage initiation, and an energy-based damage evolution law based on a model-independent fracture criterion is selected for damage propagation. The traditional nonlinear finite element analysis is used to specify the crack initiation position, which is required to specify the crack location in the analysis of beams using XFEM. Three-dimensional reinforced concrete beam models are investigated subjected to three and four-point loading tests. Simply supported beams under the effect of applied static load are investigated. An elastic perfectly plastic model is used for modeling the longitudinal steel bars. The main variables considered in the study are beam depth and the shear span with beam length. The numerical results are compared with the available experimental results to demonstrate the applicability of the model. The XFEM provides the capability to predict the concrete member fracture behavior.
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Meor Ahmad, Meor Iqram, Mohd Anas Mohd Sabri, Mohd Faizal Mat Tahir, and Nur Azam Abdullah. "Predictive Modelling of Creep Crack Initiation and Growth using Extended Finite Element Method (XFEM)." Frattura ed Integrità Strutturale 16, no. 61 (June 19, 2022): 119–29. http://dx.doi.org/10.3221/igf-esis.61.08.

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In this study, a numerical strategy for predictive modelling of creep in tension tests for the rectangular plate with a single crack and CT-specimen based on the extended finite element method (XFEM) will be described in detail. A model of creep fracture initiation and creep crack growth (CCG) is developed, while the XFEM is employed to spots located inside the finite element for the purpose of predicting crack potential and propagation. In order to characterize the creep fracture initiation, identification of C(t)-integral formula is conducted. In addition, XFEM and analytical solutions are also analyzed to look at the connection of C(t)-integral with time for a rectangular plate with a single crack under plane stress conditions. An illustration showing the se-quence of stress distribution and displacement contour plots are also being presented. The stresses and displacements spread throughout the crack path have also been determined using CT-specimens. In addition, the creep cracks growth length with normalized time and the creep crack growth rate with the C(t)-integral are predicted to be related, indicating that the numerical results are in good accord with the experimental results.
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Schmidt, Patrick, D. M. Pedroso, Hans Mühlhaus, and Alexander Scheuermann. "Assessment of a Method to Model 2D Discontinuities with Enriched Finite Elements and Level Sets." Applied Mechanics and Materials 846 (July 2016): 391–96. http://dx.doi.org/10.4028/www.scientific.net/amm.846.391.

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The computational treatment of discontinuities within the framework of the finite element method (FEM) is a requirement for simulations of fracturing of solids and has become a challenging topic in computational mechanics. Particularly popular amongst the advanced schemes is the extended finite element method (XFEM) which is based on enrichment of shape functions and falls within the framework of the partition of unity method. Because there is no simple way to track the interface of discontinuities, the computer implementation of the XFEM is not as straightforward as the FEM. One method to solve the interface tracking problem is the level set method (LSM) which introduces another partial differential equation. The level set equation describes the change of an interface due to a known velocity field. To obtain its solution, the FEM can also be employed. This contribution investigates the XFEM-LSM technique with element enrichment and the integration of discontinuous elements for the modelling of cracks or material interfaces. Numerical experiments illustrate the capabilities and accuracy of the resulting formulation.
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Chen, Zhanglan, Jianmin Liu, and Haijun Qiu. "Solidification Crack Evolution in High-Strength Steel Welding Using the Extended Finite Element Method." Materials 13, no. 2 (January 19, 2020): 483. http://dx.doi.org/10.3390/ma13020483.

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High-strength steel suffers from an increasing susceptibility to solidification cracking in welding due to increasing carbon equivalents. However, the cracking mechanism is not fully clear for a confidently completely crack-free welding process. To present a full, direct knowledge of fracture behavior in high-strength steel welding, a three-dimensional (3-D) modeling method is developed using the extended finite element method (XFEM). The XFEM model and fracture loads are linked with the full model and the output of the thermo-mechanical finite element method (TM-FEM), respectively. Solidification cracks in welds are predicted to initiate at the upper tip at the current cross-section, propagate upward to and then through the upper weld surface, thereby propagating the lower crack tip down to the bottom until the final failure. This behavior indicates that solidification cracking is preferred on the upper weld surface, which has higher weld stress introduced by thermal contraction and solidification shrinkage. The modeling results show good agreement with the solidification crack fractography and in situ observations. Further XFEM results show that the initial defects that exhibit higher susceptibility to solidification cracking are those that are vertical to the weld plate plane, open to the current cross-section and concentratedly distributed compared to tilted, closed and dispersedly distributed ones, respectively.
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Sima, Yu Zhou, and Fu Zhou Wang. "Analysis of Multi-Crack Growth in Asphalt Pavement Based on Extended Finite Element Method." Advanced Materials Research 588-589 (November 2012): 1926–29. http://dx.doi.org/10.4028/www.scientific.net/amr.588-589.1926.

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An extended finite element method (XFEM) for multiple crack growth in asphalt pavement is described. A discontinuous function and the two-dimensional asymptotic crack-tip displacement fields are added to the finite element approximation to account for the crack using the notion of partition of unity. This enables the domain to be modeled by finite element with no explicit meshing of the crack surfaces. Computational geometry issues associated with the representation of the crack and the enrichment of the finite element approximation are discussed. Finally, the propagation path of the cracks in asphalt pavement under different load conditions is presented.
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Xiaoge, Tian, Ren Zhang, Zhen Yang, Yantian Chu, Shaohua Zhen, and Yichao Xv. "Simulation of Bending Fracture Process of Asphalt Mixture Semicircular Specimen with Extended Finite Element Method." Advances in Materials Science and Engineering 2018 (October 17, 2018): 1–8. http://dx.doi.org/10.1155/2018/4081264.

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In order to numerically simulate the whole fracture process including the initiation and propagation of crack in asphalt concrete semicircular specimens under external force, the extended finite element method (XFEM) was adopted considering the shortcomings of the conventional finite element method (FEM). The fracture processes of the semicircular specimens under 5 kinds of loading modes, Me, were analyzed, and the simulation results were compared to the actual fracture paths in the actual specimens. The results indicated that the critical effective stress intensity factor will decrease first and then increase with the increase of Me, and the XFEM simulation results are similar to that of the actual specimens in crack initiation angle and propagation path in the 5 different loading modes. It is proved that the XFEM is very effective in simulating the fracture process and has obvious advantages compared with the FEM. According to the stress state at the crack tip, the initiation angle and its propagation paths were analyzed, and it was pointed out that the increase of the shear stress component caused the crack initial angle to increase with the increase of Me.
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Yu, Tian Tang, and Lu Yang Shi. "On XFEM Applications to Crack Surface under External Force." Applied Mechanics and Materials 152-154 (January 2012): 210–15. http://dx.doi.org/10.4028/www.scientific.net/amm.152-154.210.

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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.
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Duan, Nana, Xinyu Ma, Shaocong Lu, Weijie Xu, and Shuhong Wang. "Research on 3D Improved Extended Finite Element Method for Electric Field of Liquid Nitrogen with Bubbles." Applied Sciences 11, no. 11 (May 25, 2021): 4839. http://dx.doi.org/10.3390/app11114839.

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In this paper, the improved extended finite element method (XFEM) for analyzing the three-dimensional (3D) electric field is presented. The interface between two media is described by using a four-dimensional (4D) level set function. For elements with multiple interfaces, the local level set method is used to improve the accuracy. By using weak discontinuous enrichment function and moving level set function, the interpolation function is modified. The new interpolation function makes it unnecessary to repeat the mesh generation when a moving interface occurs. The cost of calculation is greatly reduced. The reliability of 3D improved XFEM in the electric field is verified through numerical calculation examples of single bubble, multi-bubbles, and moving deformed bubble in liquid nitrogen.
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Pirboudaghi, Sajjad, Reza Tarinejad, and Mohammad Taghi Alami. "Damage detection based on system identification of concrete dams using an extended finite element–wavelet transform coupled procedure." Journal of Vibration and Control 24, no. 18 (July 26, 2017): 4226–46. http://dx.doi.org/10.1177/1077546317722428.

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The aim of the present study is to propose a procedure for seismic cracking identification of concrete dams using a coupling of the extended finite element method (XFEM) based on cohesive crack segments (XFEM-COH) and continuous wavelet transform (CWT). First, the dam is numerically modeled using the traditional finite element method (FEM). Then, cracking capability is added to the dam structure by applying the XFEM-COH for concrete material. The results of both the methods under the seismic excitation have been compared and identified to damage detection purposes. In spite of predefined damage in some of the structural health monitoring (SHM) techniques, there is an advantage in the XFEM model where the whole dam structure is potentially under damage risk without initial crack, and may not crack at all. Finally, in order to evaluate any change in the system, that is, specification of any probable crack effects and nonlinear behavior, the structural modal parameters and their variation have been investigated using system identification based on the CWT. The results show that the extended finite element–wavelet transform procedure has high ability for the online SHM of concrete dams that by analysis of its results, the history of physical changes, cracking initiation time, and exact damage localization have been performed from comparing the intact (FEM) and damaged (XFEM) modal parameters of the structural response. In addition, any small change in the system is observable while the final crack profile and performance simulation of the dam body under strong seismic excitations have obtained.
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