Advertisement

Earthquake Engineering and Engineering Vibration

, Volume 16, Issue 4, pp 859–881 | Cite as

A sophisticated simulation for the fracture behavior of concrete material using XFEM

  • Changhai Zhai
  • Xiaomin Wang
  • Jingchang Kong
  • Shuang Li
  • Lili Xie
Technical Papers

Abstract

The development of a powerful numerical model to simulate the fracture behavior of concrete material has long been one of the dominant research areas in earthquake engineering. A reliable model should be able to adequately represent the discontinuous characteristics of cracks and simulate various failure behaviors under complicated loading conditions. In this paper, a numerical formulation, which incorporates a sophisticated rigid-plastic interface constitutive model coupling cohesion softening, contact, friction and shear dilatation into the XFEM, is proposed to describe various crack behaviors of concrete material. An effective numerical integration scheme for accurately assembling the contribution to the weak form on both sides of the discontinuity is introduced. The effectiveness of the proposed method has been assessed by simulating several well-known experimental tests. It is concluded that the numerical method can successfully capture the crack paths and accurately predict the fracture behavior of concrete structures. The influence of mode-II parameters on the mixed-mode fracture behavior is further investigated to better determine these parameters.

Keywords

fracture behavior concrete material earthquake engineering interface constitutive model XFEM 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Notes

Acknowledgement

The authors want to express their sincere gratitude to P. Benson Shing of the University of California at San Diego and Ioannis Koutromanos of Virginia Polytechnic Institute and State University for their kindly help. This investigation is supported by the Scientific Research Fund of Institute of Engineering Mechanics, China Earthquake Administration (No. 2016A01), the National Key Research and Development Plan (No. 2016YFC0701108), the National Natural Science Foundation of China (Nos. 51238012, 51322801), the Outstanding Talents Jump Promotion Plan of Basic Research of Harbin Institute of Technology. This support is greatly appreciated.

References

  1. Abdelaziz Y and Hamouine A (2008), “A Survey of the Extended Finite Element.” Computers and Structures, 86(11-12): 1141–1151.CrossRefGoogle Scholar
  2. Abedi R, Hawker MA, Haber RB and Matous K (2010), “An Adaptive Spacetime Discontinuous Galerkin Method for Cohesive Models of Elastodynamic Fracture.” International Journal for Numerical Methods in Engineering, 81: 1207–1241.Google Scholar
  3. Arrea M and Ingraffea AR (1982), “Mixed-mode Crack Propagation in Mortar and Concrete.” Report No. 81-13, Department of Structural Engineering, Cornell University.Google Scholar
  4. Asferg J, Poulsen P and Nielsen L (2007), “A Consistent Partly Cracked XFEM Element for Cohesive Crack Growth.” International Journal for Numerical Methods in Engineering, 72: 464–485.CrossRefGoogle Scholar
  5. Barenblatt GI (1962), “The Mathematical Theory of Equilibrium of Cracks in Brittle Fracture.” Advances in Applied Mechanics, 7: 55–129.CrossRefGoogle Scholar
  6. Bazant ZP and Ozbolt J (1990), “Nonlocal Microplane for Fracture, Damage and Size Effect in Structures.” Journal of Engineering Mechanics, 116: 2485–2504.CrossRefGoogle Scholar
  7. Bazant ZP and Pijaudier-Cabot G (1988), “Nonlocal Continuum Damage, Localization Instability and Convergence.” Journal of Applied Mechanics, 55(6): 287–293.CrossRefGoogle Scholar
  8. Bechet E, Minnebo H, Moes N and Burgardt B (2005), “Improved Implementation and Robustness Study of the X-FEM for Stress Analysis Around Cracks.” International Journal for Numerical Methods in Engineering, 64(14): 1033–1056.CrossRefGoogle Scholar
  9. Belytschko T, Moes N, Usui S and Parimi C (2001), “Arbitrary Discontinuities in Finite Elements.” International Journal for Numerical Methods in Engineering, 50: 993–1013.CrossRefGoogle Scholar
  10. Bobinski J and Tejchman J (2012), “Application of Extended Finite Element Method to Cracked Concrete Elements -Numerical Aspects.” Archives of Civil Engineering, 58(4): 409–431.CrossRefGoogle Scholar
  11. Bocca P, Carpinteri A and Valente S (1991), “Mixed Mode Fracture of Concrete.” International Journal of Solids and Structures, 27(9): 1139–1153.CrossRefGoogle Scholar
  12. Bordas S, Nguyen V, Dunant C, Nguyen-Dang H and Guidoum A (2007), “An Extended Finite Element Library.” International Journal for Numerical Methods in Engineering, 71(6): 703–732.CrossRefGoogle Scholar
  13. Camacho GT and Ortiz M (1996), “Computational Modelling of Impact Damage in Brittle Materials.” International Journal of Solids Structures, 33(20-22): 2899–2938.CrossRefGoogle Scholar
  14. Carol I, Prat PC and Lopez CM (1997), “Normal/Shear Cracking Model: Application to Discrete Crack Analysis.” Journal of Engineering Mechanics, 123(8): 762–773.CrossRefGoogle Scholar
  15. Cendon DA, Galvez JC, Elices M and Planas J (2000), “Modelling the Fracture of Concrete under Mixed Loading.” International Journal of Fracture, 103: 293–310.CrossRefGoogle Scholar
  16. Cervenka J (1994), “Mixed-mode Discrete Crack Propagation in Concrete Structures.” PhD Thesis, Department of Civil, Architectural and Environmental Engineering, University of Colorado at Boulder.Google Scholar
  17. Chen Hao, Xie Quancai, Dai Boyang, Zhang Haoyu and Chen Hongfu (2016), “Seismic Damage to Structures in the Ms6.5 Ludian Earthquake,” Earthquake Engineering and Engineering Vibration, 15(1): 173–186. DOI:10.1007/s11803-016-0314-4.CrossRefGoogle Scholar
  18. Comi C and Mariani S (2007), “Extended Finite Element Simulation of Quasi-brittle Fracture in Functionally Graded Materials.” Computer methods in Applied Mechanics and Engineering, 196: 4013–4026.CrossRefGoogle Scholar
  19. Cox JV (2009), “An Extended Finite Element Method with Analytical Enrichment for Cohesive Crack Modeling.” International Journal for Numerical Methods in Engineering, 78: 48–83.CrossRefGoogle Scholar
  20. de Borst R (2002), “Some Recent Issues in Computational Failure Mechanics.” International Journal for Numerical Methods in Engineering, 52: 63–95.CrossRefGoogle Scholar
  21. Dolbow J, Moes N and Belytschko T (2001), “An Extended Finite Element Method for Modelling Crack Growth with Frictional Contact.” Computer Methods in Applied Mechanics and Engineering, 190: 6825–6846.CrossRefGoogle Scholar
  22. Dugdale DS (1960), “Yielding of Steel Sheets Containing Slits.” Journal of the Mechanics and Physics of Solids, 8: 100–104.CrossRefGoogle Scholar
  23. Ferrara L and di Prisco M (2001), “Mode I Fracture Behavior in Concrete: Nonlocal Damage Modelling.” Journal of Engineering Mechanics, 127: 678–692.CrossRefGoogle Scholar
  24. Fremond M and Nedjar B (1996), “Damage, Gradient of Damage and Principle of Virtual Power.” International Journal of Solids and Structures, 33(8): 108–1103.CrossRefGoogle Scholar
  25. Fries TP and Belytschko T (2010), “The Extended/Generalized Finite Element Method: An Overview of the Method and Its Applications.” International Journal for Numerical Methods in Engineering, 84: 253–304.Google Scholar
  26. Galvez JC, Elices M, Guinea GV and Planas J (1996), “Crack Trajectories under Mixed-mode and Nonproportional Loading.” International Journal of Fracture, 81: 171–193.CrossRefGoogle Scholar
  27. Galvez JC, Elices M, Guinea GV and Planas J (1998), “Mixed-mode Fracture of Concrete under Proportional and Non-proportional Loading.” International Journal of Fracture, 94: 267–284.CrossRefGoogle Scholar
  28. Gerstle WH and Xie M (1992), “FEM Modelling of Fictitious Crack Propagation in Concrete.” Journal of Engineering Mechanics, 118(2): 416–434.CrossRefGoogle Scholar
  29. Hassanzadeh M (1990), “Determination of Fracture Zone Properties in Mixed Mode I and II.” Engineering Fracture Mechanics, 35(4-5): 845–853.CrossRefGoogle Scholar
  30. Hillerborg A, Moder M and Petersson PE (1976), “Analysis of Crack Formation and Crack Growth in Concrete by Means of Fracture Mechanics and Finite Elements.” Cement and Concrete Research, 6: 773–782.CrossRefGoogle Scholar
  31. Jaskowiec J and van der Meer FP (2014), “A Consistent Iterative Scheme for 2D and 3D Cohesive Crack Analysis in XFEM.” Computers and Structures, 136: 98–107.CrossRefGoogle Scholar
  32. Jirasek M and Zimmermann TH (1998) “Rotating Crack Model with Transition to Scalar Damage.” Journal Engineering Mechanics, 124(3): 277–284.CrossRefGoogle Scholar
  33. Khoei AR (2015), “Extended Finite Element Method: Theory and Applications.” Wiley.Google Scholar
  34. Koutromanos I (2011), “Numerical Analysis of Masonryinfilled Reinforced Concrete Frames Subjected to Seismic Loads and Experimental Evaluation of Retrofit Techniques.” PhD Thesis, Department of Structural Engineering, University of California at San Diego.Google Scholar
  35. Kuutti J and Kolari K (2012), “A Local Remeshing Procedure to Simulate Crack Propagation in Quasi-brittle Materials.” Engineering Computations: International Journal for Couputer-Aided Engineering and Software, 29(2): 125–143.CrossRefGoogle Scholar
  36. Li B (2014), “Numerical and Experimental Analysis of Crack Propagation Behavior for Ceramic Materials.” Materials Research Innovations, 18(6): 418–429.CrossRefGoogle Scholar
  37. Lin Xuchuan, Zhang Haoyu, Chen Hongfu, Chen Hao and Lin Junqi (2015), “Field Investigation on Severely Damaged Aseismic Buildings in 2014 Ludian Earthquake,” Earthquake Engineering and Engineering Vibration, 14(1): 169–176. DOI: 10.1007/s11803-015-0014-5.CrossRefGoogle Scholar
  38. Linder C and Armero F (2007), “Finite Elements with Embedded Strong Discontinuities for the Modelling of Failure in Solids.” International Journal for Numerical Methods in Engineering, 72(3): 1391–1433.CrossRefGoogle Scholar
  39. Lotfi HR and Shing PB (1994), “Interface Model Applied to Fracture of Masonry Structures.” Journal of Structural Engineering, 120(1): 63–80.CrossRefGoogle Scholar
  40. Mariani S and Perego U (2003), “Extended Finite Element Method for Quasi-brittle Fracture.” International Journal for Numerical Methods in Engineering, 58: 103–126.CrossRefGoogle Scholar
  41. Mehrabi AB and Shing PB (1997), “Finite Element Modelling of Masonry-infilled RC Frames.” Journal of Structural Engineering, 123(5): 604–613.CrossRefGoogle Scholar
  42. Melenk JM and Babuska I (1996), “The Partition of Unity Finite Element Method: Basic Theory and Applications.” Computer Methods in Applied Mechanics and Engineering, 39: 289–314.CrossRefGoogle Scholar
  43. Mergheim J, Kuhl E and Steinmann P (2005), “A Finite Element Method for the Computational Modelling of Cohesive Cracks.” International Journal for Numerical Methods in Engineering, 63: 276–289.CrossRefGoogle Scholar
  44. Meschke G and Dumstorff P (2007), “Energy-based Modelling of Cohesive and Cohesionless Cracks via X-FEM.” Computer Methods in Applied Mechanics and Engineering, 196: 2338–2357.CrossRefGoogle Scholar
  45. Moes N and Belytschko T (2002), “Extended Finite Element Method for Cohesive Crack Growth.” Engineering Fracture Mechanics, 69: 813–833.CrossRefGoogle Scholar
  46. Moes N, Dolbow J and Belytschko T (1999), “A Finite Element Method for Crack Growth Without Remeshing.” International Journal for Numerical Methods in Engineering, 46: 131–150.CrossRefGoogle Scholar
  47. Needleman A (2014), “Some Issues in Cohesive Surface Modeling.” Procedia IUTAM, 10: 221–246.CrossRefGoogle Scholar
  48. Oliveira DV and Lourenco PB (2004), “Implementation and Validation of A Constitutive Model for the Cyclic Behaviour of Interface Elements,” Computers and Structures, 82: 1451–1461.CrossRefGoogle Scholar
  49. Ortiz M and Pandolfi A (1999), “Finite-deformation Irreversible Cohesive Elements for Three-dimensional Crack-propagation Analysis.” International Journal for Numerical Methods in Engineering, 44: 1267–1282.CrossRefGoogle Scholar
  50. Ozbolt J and Reinhardt HW (2002), “Numerical Study of Mixed-mode Fracture in Concrete.” International Journal of Fracture, 118: 145–161.CrossRefGoogle Scholar
  51. Peerlings RHJ, de Borst R, Brekelmans WAM and Geers MGD (1998), “Gradient-enhanced Damage Modeling of Concrete Fracture.” Mechanics of Cohesive-Frictional Meterials, 3: 323–342.CrossRefGoogle Scholar
  52. Pommier S, Gravouil A, Combescure A and Moes N (2011), “Extended Finite Element Method for Crack Propagation.” Wiley-ISTE.Google Scholar
  53. Puntel E, Bolzon G and Saouma VE (2006), “Fracture Mechanics Based Model for Joints under Cyclic Loading.” Journal of Engineering Mechanics, 132(11): 1151–1159.CrossRefGoogle Scholar
  54. Reinhardt HW (1984), “Fracture Mechanics of an Elastic Softening Material Like Concrete.” Heron 29(2). Delft, the Netherlands, 1–42.Google Scholar
  55. Remmers JJC, de Borst R and Needleman A (2003), “A Cohesive Segments Method for the Simulation of Crack Growth.” Computational Mechanics, 31: 69–77.CrossRefGoogle Scholar
  56. Rethore J, Gravouil A and Combescure A (2005), “An Energy-conserving Scheme for Dynamic Crack Growth Using the Extended Finite Element Method.” International Journal for Numerical Methods in Engineering, 63: 631–659.CrossRefGoogle Scholar
  57. Rots JG and de Borst R (1987), “Analysis of Mixed-Mode Fracture in Concrete.” Journal of Engineering Mechanics, 113(11): 1739–1758.CrossRefGoogle Scholar
  58. Saleh AL and Aliabadi MH (1995), “Crack Growth Analysis in Concrete Using Boundary Element Method.” Engineering Fracture Mechanics, 51(4): 533–545.CrossRefGoogle Scholar
  59. Stankowski T, Runesson K and Sture S (1993), “Fracture and Slip of Interfaces in Cementitious Composites, I: Characteristics.” Journal of Engineering Mechanics, 119(2): 292–314.CrossRefGoogle Scholar
  60. Stolarska M, Chopp DL, Moes N and Belytschko T (2001), “Modelling Crack Growth by Level Sets in the Extended Finite Element Method.” International Journal for Numerical Methods in Engineering, 51: 943–960.CrossRefGoogle Scholar
  61. Sukumar N and Prevost JH (2003), “Modeling Quasistatic Crack Growth with the Extended Finite Element Method Part I: Computer Implementation.” International Journal of Solids and Structures, 40: 7513–7537.CrossRefGoogle Scholar
  62. Swartz SE, Lu L, Tang L and Refai T (1988), “Mode-II Fracture Parameter Estimates for Concrete from Beam Specimens.” Experimental Mechanics, 28: 146–153.CrossRefGoogle Scholar
  63. Wittmann FH (2002), “Crack Formation and Fracture Energy of High Strength Concrete.” Sadhana Academy Proceedings in Engineering Sciences, 27(4): 413–423.Google Scholar
  64. Wells GN and Sluys LJ (2001), “A New Method for Modelling Cohesive Cracks Using Finite Elements.” International Journal for Numerical Methods in Engineering, 50: 2667–2682.CrossRefGoogle Scholar
  65. Wu JY, Li FB and Xu SL (2015), “Extended Embedded Finite Elements with Continuous Displacement Jumps for the Modeling of Localized Failure in Solids.” Computer Methods in Applied Mechanics and Engineering, 285: 346–378.CrossRefGoogle Scholar
  66. Xiao QZ, karihaloo BL and Liu XY (2007), “Incrementalsecant Modulus Iteration Scheme and Stress Recovery for Simulating Cracking Process in Quasi-brittle Materials Using XFEM.” International Journal for Numerical Methods in Engineering, 69: 2606–2635.CrossRefGoogle Scholar
  67. Xu XP and Needleman A (1994), “Numerical Simulations of Fast Crack Growth in Brittle Solids.” Journal of the Mechanics and Physics of Solids, 42(9): 1397–1434.CrossRefGoogle Scholar
  68. Zamani A, Gracie R and Eslami MR (2012), “Cohesive and Non-cohesive Fracture by Higher-order Enrichment of XFEM.” International Journal for Numerical Method in Engineering, 90: 452–483.CrossRefGoogle Scholar
  69. Zhang XD and Bui TQ (2015), “A Fictitious Crack XFEM with Two New Solution Algorithms for Cohesive Crack Growth Modeling in Concrete Structures.” Engineering Computations: International Journal for Couputer-Aided Engineering and Software, 32(2): 473–497.CrossRefGoogle Scholar
  70. Zhao Y and Wang FL (2015), “Experimental Studies on Behavior of Fully Grouted Reinforced-concrete Masonry Shear Walls,” Earthquake Engineering and Engineering Vibration, 14(4): 743–757. DOI10.1007/s11803-015-0030-5CrossRefGoogle Scholar

Copyright information

© Institute of Engineering Mechanics, China Earthquake Administration and Springer-Verlag GmbH Germany 2017

Authors and Affiliations

  • Changhai Zhai
    • 1
    • 2
  • Xiaomin Wang
    • 1
    • 2
  • Jingchang Kong
    • 1
    • 2
  • Shuang Li
    • 1
    • 2
  • Lili Xie
    • 1
    • 3
  1. 1.School of Civil EngineeringHarbin Institute of TechnologyHarbinChina
  2. 2.Key Lab of Structures Dynamic Behavior and Control (Harbin Institute of Technology)Ministry of EducationHeilongjiang, HarbinChina
  3. 3.Institute of Engineering MechanicsChina Earthquake AdministrationHarbinChina

Personalised recommendations