Simulation of cohesive crack growth by a variable-node XFEM

doi:10.1007/s11709-019-0595-6

Front. Struct. Civ. Eng.

2020, Vol. 14

Issue (1) : 215-228 https://doi.org/10.1007/s11709-019-0595-6

RESEARCH ARTICLE

Simulation of cohesive crack growth by a variable-node XFEM

Weihua FANG¹, Jiangfei WU², Tiantang YU²(

), Thanh-Tung NGUYEN³, Tinh Quoc BUI^4,⁵(

)

¹. Nanjing Automation Institute of Water Conservancy and Hydrology, Nanjing 210012, China
². Department of Engineering Mechanics, Hohai University, Nanjing 211100, China
³. Laboratory of Solid Structures, University of Luxembourg, Luxembourg L-1359, Luxembourg
⁴. Institute for Research and Development, Duy Tan University, Da Nang City 550000, Vietnam
⁵. Department of Civil and Environmental Engineering, Tokyo Institute of Technology, Tokyo 152-8552, Japan

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Abstract

A new computational approach that combines the extended finite element method associated with variable-node elements and cohesive zone model is developed. By using a new enriched technique based on sign function, the proposed model using 4-node quadrilateral elements can eliminate the blending element problem. It also allows modeling the equal stresses at both sides of the crack in the crack-tip as assumed in the cohesive model, and is able to simulate the arbitrary crack-tip location. The multiscale mesh technique associated with variable-node elements and the arc-length method further improve the efficiency of the developed approach. The performance and accuracy of the present approach are illustrated through numerical experiments considering both mode-I and mixed-mode fracture in concrete.

Keywords extended finite element method cohesive zone model sign function crack propagation

Corresponding Author(s): Tiantang YU,Tinh Quoc BUI

Just Accepted Date: 28 October 2019 Online First Date: 17 December 2019 Issue Date: 21 February 2020

Cite this article:

Weihua FANG,Jiangfei WU,Tiantang YU, et al. Simulation of cohesive crack growth by a variable-node XFEM[J]. Front. Struct. Civ. Eng., 2020, 14(1): 215-228.

URL:

https://academic.hep.com.cn/fsce/EN/10.1007/s11709-019-0595-6
https://academic.hep.com.cn/fsce/EN/Y2020/V14/I1/215

Fig.1 Schematic illustration of the investigated problem: a solid domain containing a crack, in which the process zone exists at the crack tip. (a) A solid domain with a crack; (b) zoom in the region of the cohesive zone.

Fig.2 Schematic representation of a linear cohesive law adopted to this study.

Fig.3 Nodal discontinuous displacement field for the crack-tip element: (a) displacement field at the nodes 1 and 4; (b) the corresponding isoparametric element.

Fig.4 Meshes representation of two different scale elements. The crosshatched lines show one layer of variable node elements.

Fig.5 A schematic illustration for a (4+ k + m)-node element.

Fig.6 Description of the three-point bending test: geometry and boundary conditions.

Fig.7 Three different meshes used to perform the numerical simulation: (a) coarse scale mesh, (b) fine scale mesh, (c) multiscale mesh.

Fig.8 Comparison of the mechanical response between the reference data and the numerical prediction by the present model for different meshes.

Tab.1 Mode-I fracture test: comparison of the numerical performance for different meshes

Fig.9 Crack propagation for different loadings (a scaling factor of 200 is used to plot this figure). (a) P = 5.529 kN; (b) P = 3.804 kN; (c) P = 1.961 kN; (d) P = 0.238 kN.

Fig.10 Mixed-mode fracture test of a simple supported beam: geometry, and boundary conditions.

Fig.11 Three different meshes used to perform the numerical simulation: (a) coarse scale mesh, (b) fine scale mesh, (c) multiscale mesh.

Fig.12 Propagation of crack for different loadings (scaling factor 160). (a) P = 3.706 kN; (b) P = 3.243 kN; (c) P = 1.898kN; (d) P = 0.457 kN.

Fig.13 Comparison of the final crack paths.

Tab.2 Mixed-mode fracture test: comparison of the numerical performance for different meshes

Fig.14 Comparison of the load-CMOD curves obtained from the present model with the reference data in Ref. [⁴⁷].

Fig.15 Two different irregular meshes used to perform the numerical simulation: (a) fine scale mesh; (b) multiscale mesh.

Fig.16 The load-CMOD curves obtained from the present model with two irregular meshes.

Fig.17 Description of the mixed-mode fracture test: geometry, and boundary conditions.

Fig.18 Three different meshes used to perform the numerical simulation: (a) coarse scale mesh; (b) fine scale mesh; (c) multiscale mesh.

Fig.19 Comparison of the final crack path obtained from different mesh with the reference result in Ref. [⁴⁷].

Fig.20 Comparison of the mechanical response: load-CMOD curves obtained from different meshes.

1	T Belytschko, T Black. Elastic crack growth in finite elements with minimal remeshing. International Journal for Numerical Methods in Engineering, 1999, 45(5): 601–620 https://doi.org/10.1002/(SICI)1097-0207(19990620)45:5<601::AID-NME598>3.0.CO;2-S
2	N Moës, J Dolbow, T Belytschko. A finite element method for crack growth without remeshing. International Journal for Numerical Methods in Engineering, 1999, 46(1): 131–150 https://doi.org/10.1002/(SICI)1097-0207(19990910)46:1<131::AID-NME726>3.0.CO;2-J
3	G Yi, T T Yu, T Q Bui, S Tanaka. Bi-material V-notched SIFs analysis by XFEM and conservative integral approach. Computers & Structures, 2018, 196: 217–232
4	T T Yu, T Q Bui. Numerical simulation of 2-D weak and strong discontinuities by a novel approach based on XFEM with local mesh refinement. Computers & Structures, 2018, 196: 112–133 https://doi.org/10.1016/j.compstruc.2017.11.007
5	C P Ma, T T Yu, L V Lich, T Q Bui. An effective computational approach based on XFEM and a novel three-step detection algorithm for multiple complex flaw clusters. Computers & Structures, 2017, 193: 207–225
6	G Yi, T T Yu, T Q Bui, C P Ma, S Hirose. SIFs evaluation of sharp V-notched fracture by XFEM and strain energy approach. Theoretical and Applied Fracture Mechanics, 2017, 89: 35–44 https://doi.org/10.1016/j.tafmec.2017.01.005
7	Z Wang, T T Yu, T Q Bui, S Tanaka, C Zhang, S Hirose, J L Curiel-Sosa. 3-D local mesh refinement XFEM with variable-node hexahedron elements for extraction of stress intensity factors of straight and curved planar cracks. Computer Methods in Applied Mechanics and Engineering, 2017, 313: 375–405 https://doi.org/10.1016/j.cma.2016.10.011
8	Z Wang, T T Yu, T Q Bui, N A Trinh, N T H Luong, N D Duc, D H Doan. Numerical modeling of 3-D inclusions and voids by a novel adaptive XFEM. Advances in Engineering Software, 2016, 102: 105–122 https://doi.org/10.1016/j.advengsoft.2016.09.007
9	T T Yu, T Q Bui, S H Yin, D H Doan, C T Wu, T V Do, S Tanaka. On the thermal buckling analysis of functionally graded plates with internal defects using extended isogeometric analysis. Composite Structures, 2016, 136: 684–695 https://doi.org/10.1016/j.compstruct.2015.11.002
10	T T Yu, T Q Bui, P Liu, C Zhang, S Hirose. Interfacial dynamic impermeable cracks analysis in dissimilar piezoelectric materials under coupled electromechanical loading with the extended finite element method. International Journal of Solids and Structures, 2015, 67–68: 205–218 https://doi.org/10.1016/j.ijsolstr.2015.03.037
11	L Y Shi, T T Yu, T Q Bui. Numerical modeling of hydraulic fracturing in rock mass by XFEM. Soil Mechanics and Foundation Engineering, 2015, 52(2): 74–83 https://doi.org/10.1007/s11204-015-9309-9
12	P Liu, T Q Bui, D Zhu, T T Yu, J W Wang, S H Yin, S Hirose. Buckling failure analysis of cracked functionally graded plates by a stabilized discrete shear gap extended 3-node triangular plate element. Composites. Part B, Engineering, 2015, 77: 179–193 https://doi.org/10.1016/j.compositesb.2015.03.036
13	P Liu, T T Yu, T Q Bui, C Zhang, Y P Xu, C W Lim. Transient thermal shock fracture analysis of functionally graded piezoelectric materials by the extended finite element method. International Journal of Solids and Structures, 2014, 51(11–12): 2167–2182 https://doi.org/10.1016/j.ijsolstr.2014.02.024
14	T T Yu. The extended finite element method (XFEM) for discontinuous rock masses. Engineering Computations, 2011, 28(3): 340–369 https://doi.org/10.1108/02644401111118178
15	S Liu, T Yu, L Van Lich, S Yin, T Q Bui. Size effect on cracked functional composite micro-plates by an XIGA-based effective approach. Meccanica, 2018, 53(10): 2637–2658 https://doi.org/10.1007/s11012-018-0848-9
16	Z P Bažant, J Planas. Fracture and Size Effect in Concrete and Other Quasibrittle Materials. Boca Raton: CRC Press, 1998
17	D S Dugdale. Yielding of steel sheets containing slits. Journal of the Mechanics and Physics of Solids, 1960, 8(2): 100–104 https://doi.org/10.1016/0022-5096(60)90013-2
18	G I Barenblatt. The mathematical theory of equilibrium of cracks in brittle fracture. Advances in Applied Mechanics, 1962, 7: 55–129 https://doi.org/10.1016/S0065-2156(08)70121-2
19	A Hillerborg, M Modéer, P E Petersson. Analysis of crack formation and crack growth in concrete by means of fracture mechanics and finite elements. Cement and Concrete Research, 1976, 6(6): 773–781 https://doi.org/10.1016/0008-8846(76)90007-7
20	F Barpi, S Valente. The cohesive frictional crack model applied to the analysis of the dam-foundation joint. Engineering Fracture Mechanics, 2010, 77(11): 2182–2191 https://doi.org/10.1016/j.engfracmech.2010.02.030
21	B Yang, K Ravi-Chandar. A single-domain dual-boundary-element formulation incorporating a cohesive zone model for elastostatic cracks. International Journal of Fracture, 1998, 93(1/4): 115–144 https://doi.org/10.1023/A:1007535407986
22	T Belytschko, D Organ, C Gerlach. Element-free galerkin methods for dynamic fracture in concrete. Computer Methods in Applied Mechanics and Engineering, 2000, 187(3–4): 385–399 https://doi.org/10.1016/S0045-7825(00)80002-X
23	J M Sancho, J Planas, A M Fathy, J C Gálvez, D A Cendón. Three-dimensional simulation of concrete fracture using embedded crack elements without enforcing crack path continuity. International Journal for Numerical and Analitical Methods in Geomechanics, 2007, 31(2): 173–187 https://doi.org/10.1002/nag.540
24	G N Wells, L J Sluys. A new method for modeling cohesive cracks using finite elements. International Journal for Numerical Methods in Engineering, 2001, 50(12): 2667–2682 https://doi.org/10.1002/nme.143
25	J L Asferg, P N Poulsen, L O Nielsen. A consistent partly cracked XFEM element for cohesive crack growth. International Journal for Numerical Methods in Engineering, 2007, 72(4): 464–485 https://doi.org/10.1002/nme.2023
26	G Zi, T Belytschko. New crack-tip elements for XFEM and applications to cohesive cracks. International Journal for Numerical Methods in Engineering, 2003, 57(15): 2221–2240 https://doi.org/10.1002/nme.849
27	J J C Remmers, R Borst, A Needleman. A cohesive segments method for the simulation of crack growth. Computational Mechanics, 2003, 31(1–2): 69–77 https://doi.org/10.1007/s00466-002-0394-z
28	N Moës, T Belytschko. Extended finite element method for cohesive crack growth. Engineering Fracture Mechanics, 2002, 69(7): 813–833 https://doi.org/10.1016/S0013-7944(01)00128-X
29	X D Zhang, T Q Bui. A fictitious crack XFEM with two new solution algorithms for cohesive crack growth modeling in concrete structures. Engineering Computations, 2015, 32(2): 473–497 https://doi.org/10.1108/EC-08-2013-0203
30	J F Mougaard, P N Poulsen, L O Nielsen. A partly and fully cracked triangular XFEM element for modeling cohesive fracture. International Journal for Numerical Methods in Engineering, 2011, 85(13): 1667–1686 https://doi.org/10.1002/nme.3040
31	J V Cox. An extended finite element method with analytical enrichment for cohesive crack modeling. International Journal for Numerical Methods in Engineering, 2009, 78(1): 48–83 https://doi.org/10.1002/nme.2475
32	J Y Wu, F B Li. An improved stable XFEM (Is-XFEM) with a novel enrichment function for the computational modeling of cohesive cracks. Computer Methods in Applied Mechanics and Engineering, 2015, 295: 77–107 https://doi.org/10.1016/j.cma.2015.06.018
33	T Rabczuk, T Belytschko. Cracking particles: A simplified meshfree method for arbitrary evolving cracks. International Journal for Numerical Methods in Engineering, 2004, 61(13): 2316–2343 https://doi.org/10.1002/nme.1151
34	T Rabczuk, T Belytschko. A three-dimensional large deformation meshfree method for arbitrary evolving cracks. Computer Methods in Applied Mechanics and Engineering, 2007, 196(29–30): 2777–2799 https://doi.org/10.1016/j.cma.2006.06.020
35	T Rabczuk, G Zi, S Bordas, H Nguyen-Xuan. A simple and robust three-dimensional cracking-particle method without enrichment. Computer Methods in Applied Mechanics and Engineering, 2010, 199(37–40): 2437–2455 https://doi.org/10.1016/j.cma.2010.03.031
36	H Ren, X Zhuang, Y Cai, T Rabczuk. Dual-horizon peridynamics. International Journal for Numerical Methods in Engineering, 2016, 108(12): 1451–1476 https://doi.org/10.1002/nme.5257
37	H Ren, X Zhuang, T Rabczuk. Dual-horizon peridynamics: A stable solution to varying horizons. Computer Methods in Applied Mechanics and Engineering, 2017, 318: 762–782 https://doi.org/10.1016/j.cma.2016.12.031
38	T Rabczuk, R Gracie, J H Song, T Belytschko. Immersed particle method for fluid-structure interaction. International Journal for Numerical Methods in Engineering, 2010, 81(1): 48–71
39	T Rabczuk, S Bordas, G Zi. On three-dimensional modelling of crack growth using partition of unity methods. Computers & Structures, 2010, 88(23–24): 1391–1411 https://doi.org/10.1016/j.compstruc.2008.08.010
40	T Chau-Dinh, G Zi, P S Lee, T Rabczuk, J H Song. Phantom-node method for shell models with arbitrary cracks. Computers & Structures, 2012, 92–93: 242–256 https://doi.org/10.1016/j.compstruc.2011.10.021
41	J H Lim, D Sohn, S Im. Variable-node element families for mesh connection and adaptive mesh computation. Structural Engineering and Mechanics, 2012, 43(3): 349–370 https://doi.org/10.12989/sem.2012.43.3.349
42	S N Roth, P Léger, A Soulaïmani. A combined XFEM-damage mechanics approach for concrete crack propagation. Computer Methods in Applied Mechanics and Engineering, 2015, 283: 923–955 https://doi.org/10.1016/j.cma.2014.10.043
43	Y Xu, H Yuan. Computational modeling of mixed-mode fatigue crack growth using extended finite element methods. International Journal of Fracture, 2009, 159(2): 151–165 https://doi.org/10.1007/s10704-009-9391-y
44	F Liao, Z Huang. An extended finite element model for modelling localised fracture of reinforced concrete beams in fire. Computers & Structures, 2015, 152: 11–26 https://doi.org/10.1016/j.compstruc.2015.02.006
45	T T Yu. The Extended Finite Element Method-Theory, Application and Program. Beijing: Science Press, 2014
46	X F Zhang, S L Xu. Determination of fracture energy of three-point bending concrete beam using relationship between load and crack-mouth opening displacement. Journal of Hydraulic Engineering, 2008, 39(6): 714–719
47	D A Cendón, J C Gálvez, M Elices, J Planas. Modelling the fracture of concrete under mixed loading. International Journal of Fracture, 2000, 103(3): 293–310 https://doi.org/10.1023/A:1007687025575

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