Simulation of cohesive crack growth by a variable-node XFEM

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

References

[1] Belytschko T, Black T. Elastic crack growth in finite elements with minimal remeshing. International Journal for Numerical Methods in Engineering, 1999, 45(5): 601–620

[2] Moës N, Dolbow J, Belytschko T. A finite element method for crack growth without remeshing. International Journal for Numerical Methods in Engineering, 1999, 46(1): 131–150

[3] Yi G, Yu T T, Bui T Q, Tanaka S. Bi-material V-notched SIFs analysis by XFEM and conservative integral approach. Computers & Structures, 2018, 196: 217–232

[4] Yu T T, Bui T Q. 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

[5] Ma C P, Yu T T, Lich L V, Bui T Q. 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] Yi G, Yu T T, Bui T Q, Ma C P, Hirose S. SIFs evaluation of sharp V-notched fracture by XFEM and strain energy approach. Theoretical and Applied Fracture Mechanics, 2017, 89: 35–44

[7] Wang Z, Yu T T, Bui T Q, Tanaka S, Zhang C, Hirose S, Curiel-Sosa J L. 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

[8] Wang Z, Yu T T, Bui T Q, Trinh N A, Luong N T H, Duc N D, Doan D H. Numerical modeling of 3-D inclusions and voids by a novel adaptive XFEM. Advances in Engineering Software, 2016, 102: 105–122

[9] Yu T T, Bui T Q, Yin S H, Doan D H, Wu C T, Do T V, Tanaka S. On the thermal buckling analysis of functionally graded plates with internal defects using extended isogeometric analysis. Composite Structures, 2016, 136: 684–695

[10] Yu T T, Bui T Q, Liu P, Zhang C, Hirose S. 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

[11] Shi L Y, Yu T T, Bui T Q. Numerical modeling of hydraulic fracturing in rock mass by XFEM. Soil Mechanics and Foundation Engineering, 2015, 52(2): 74–83

[12] Liu P, Bui T Q, Zhu D, Yu T T, Wang J W, Yin S H, Hirose S. 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

[13] Liu P, Yu T T, Bui T Q, Zhang C, Xu Y P, Lim C W. 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

[14] Yu T T. The extended finite element method (XFEM) for discontinuous rock masses. Engineering Computations, 2011, 28(3): 340–369

[15] Liu S, Yu T, Van Lich L, Yin S, Bui T Q. Size effect on cracked functional composite micro-plates by an XIGA-based effective approach. Meccanica, 2018, 53(10): 2637–2658

[16] Bažant Z P, Planas J. Fracture and Size Effect in Concrete and Other Quasibrittle Materials. Boca Raton: CRC Press, 1998

[17] Dugdale D S. Yielding of steel sheets containing slits. Journal of the Mechanics and Physics of Solids, 1960, 8(2): 100–104

[18] Barenblatt G I. The mathematical theory of equilibrium of cracks in brittle fracture. Advances in Applied Mechanics, 1962, 7: 55–129

[19] Hillerborg A, Modéer M, Petersson P E. 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

[20] Barpi F, Valente S. The cohesive frictional crack model applied to the analysis of the dam-foundation joint. Engineering Fracture Mechanics, 2010, 77(11): 2182–2191

[21] Yang B, Ravi-Chandar K. 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

[22] Belytschko T, Organ D, Gerlach C. Element-free galerkin methods for dynamic fracture in concrete. Computer Methods in Applied Mechanics and Engineering, 2000, 187(3–4): 385–399

[23] Sancho J M, Planas J, Fathy A M, Gálvez J C, Cendón D A. 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

[24] Wells G N, Sluys L J. A new method for modeling cohesive cracks using finite elements. International Journal for Numerical Methods in Engineering, 2001, 50(12): 2667–2682

[25] Asferg J L, Poulsen P N, Nielsen L O. A consistent partly cracked XFEM element for cohesive crack growth. International Journal for Numerical Methods in Engineering, 2007, 72(4): 464–485

[26] Zi G, Belytschko T. New crack-tip elements for XFEM and applications to cohesive cracks. International Journal for Numerical Methods in Engineering, 2003, 57(15): 2221–2240

[27] Remmers J J C, Borst R, Needleman A. A cohesive segments method for the simulation of crack growth. Computational Mechanics, 2003, 31(1–2): 69–77

[28] Moës N, Belytschko T. Extended finite element method for cohesive crack growth. Engineering Fracture Mechanics, 2002, 69(7): 813–833

[29] Zhang X D, Bui T Q. A fictitious crack XFEM with two new solution algorithms for cohesive crack growth modeling in concrete structures. Engineering Computations, 2015, 32(2): 473–497

[30] Mougaard J F, Poulsen P N, Nielsen L O. A partly and fully cracked triangular XFEM element for modeling cohesive fracture. International Journal for Numerical Methods in Engineering, 2011, 85(13): 1667–1686

[31] Cox J V. An extended finite element method with analytical enrichment for cohesive crack modeling. International Journal for Numerical Methods in Engineering, 2009, 78(1): 48–83

[32] Wu J Y, Li F B. 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

[33] Rabczuk T, Belytschko T. Cracking particles: A simplified meshfree method for arbitrary evolving cracks. International Journal for Numerical Methods in Engineering, 2004, 61(13): 2316–2343

[34] Rabczuk T, Belytschko T. A three-dimensional large deformation meshfree method for arbitrary evolving cracks. Computer Methods in Applied Mechanics and Engineering, 2007, 196(29–30): 2777–2799

[35] Rabczuk T, Zi G, Bordas S, Nguyen-Xuan H. A simple and robust three-dimensional cracking-particle method without enrichment. Computer Methods in Applied Mechanics and Engineering, 2010, 199(37–40): 2437–2455

[36] Ren H, Zhuang X, Cai Y, Rabczuk T. Dual-horizon peridynamics. International Journal for Numerical Methods in Engineering, 2016, 108(12): 1451–1476

[37] Ren H, Zhuang X, Rabczuk T. Dual-horizon peridynamics: A stable solution to varying horizons. Computer Methods in Applied Mechanics and Engineering, 2017, 318: 762–782

[38] Rabczuk T, Gracie R, Song J H, Belytschko T. Immersed particle method for fluid-structure interaction. International Journal for Numerical Methods in Engineering, 2010, 81(1): 48–71

[39] Rabczuk T, Bordas S, Zi G. On three-dimensional modelling of crack growth using partition of unity methods. Computers & Structures, 2010, 88(23–24): 1391–1411

[40] Chau-Dinh T, Zi G, Lee P S, Rabczuk T, Song J H. Phantom-node method for shell models with arbitrary cracks. Computers & Structures, 2012, 92–93: 242–256

[41] Lim J H, Sohn D, Im S. Variable-node element families for mesh connection and adaptive mesh computation. Structural Engineering and Mechanics, 2012, 43(3): 349–370

[42] Roth S N, Léger P, Soulaïmani A. A combined XFEM-damage mechanics approach for concrete crack propagation. Computer Methods in Applied Mechanics and Engineering, 2015, 283: 923–955

[43] Xu Y, Yuan H. Computational modeling of mixed-mode fatigue crack growth using extended finite element methods. International Journal of Fracture, 2009, 159(2): 151–165

[44] Liao F, Huang Z. An extended finite element model for modelling localised fracture of reinforced concrete beams in fire. Computers & Structures, 2015, 152: 11–26

[45] Yu T T. The Extended Finite Element Method-Theory, Application and Program. Beijing: Science Press, 2014

[46] Zhang X F, Xu S L. 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] Cendón D A, Gálvez J C, Elices M, Planas J. Modelling the fracture of concrete under mixed loading. International Journal of Fracture, 2000, 103(3): 293–310

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