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3D fracture modelling and limit state analysis of prestressed composite concrete pipes

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Abstract

In this manuscript, we study fracture of prestressed cylindrical concrete pipes. Such concrete pipes play a major role in tunneling and underground engineering. The structure is modelled fully in 3D using three-dimensional continuum elements for the concrete structure which beam elements are employed to model the reinforcement. This allows the method to capture important phenomena compared to a pure shell model of concrete. A continuous approach to fracture is chosen when concrete is subjected to compressive loading while a combined continuous-discrete fracture method is employed in tension. The model is validated through comparisons with experimental data.

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References

  1. Bažant Z P, Pijaudier-Cabot G. Nonlocal continuum damage, localization instabilities and convergence. Journal of Engineering Mechanics, 1988, 55: 287–293

    MATH  Google Scholar 

  2. Bažant Z P. Why continuum damage is nonlocal: micromechanics arguments. Journal of Engineering mechanics, 1991, 117(5): 1070–1087

    Article  Google Scholar 

  3. Bažant Z P, Jirásek M. Non-local integral formulations of plasticity and damage: survey of process. Journal of Engineering Mechanics, 2002, 128(11): 1119–1149

    Article  Google Scholar 

  4. Chen W F. Constitutive Equations for Engineering Materials, Volume 2: Plasticity and Modeling. Amsterdam-London-New York-Tokio: Elsevier, 1994

    Google Scholar 

  5. Carol I, Bazant Z P. Damage and plasticity in microplane theory. International Journal of Solids and Structures, 1997, 34(29): 3807–3835

    Article  MATH  Google Scholar 

  6. Han W, Reddy B D. Plasticity. Mathematical theory and numerical analysis. In: Interdisciplinary Applied Mathematics. Springer, 1999

    MATH  Google Scholar 

  7. Peerlings R H J, de Borst R, Brekelmans W A M, Geers M G D. Localisation issures in local and nonlocal continuum approaches to fracture. European Journal of Mechanics–A/Solids, 2002, 21(2): 175–189

    Article  MATH  Google Scholar 

  8. Peerlings R H J, de Borst R, Brekelmans W A M, de Wree J H W. Gradient enhanced damage for quasi brittle materials. International Journal for Numerical Methods in Engineering, 1996, 39(19): 3391–3403

    Article  MATH  Google Scholar 

  9. Thai T Q, Rabczuk T, Bazilevs Y, Meschke G. A higher-order stress-based gradient-enhanced damage model based on isogeometric analysis. Computer Methods in Applied Mechanics and Engineering, 2016, 304: 584–604

    Article  MathSciNet  Google Scholar 

  10. Miehe C, Hofacker M, Welschinger F. A phase field model for rateindependent crack propagation: robust algorithmic implementation based on operator splits. Computer Methods in Applied Mechanics and Engineering, 2010, 199(45–48): 2765–2778

    Article  MathSciNet  MATH  Google Scholar 

  11. Miehe C, Welschinger F, Hofacker M. Thermodynamically consistent phasefield models of fracture: variational principles and multi-field FE implementations. International Journal for Numerical Methods in Engineering, 2010, 83(10): 1273–1311

    Article  MathSciNet  MATH  Google Scholar 

  12. Amiri F, Millán D, Shen Y, Rabczuk T, Arroyo M. Phase-field modeling of fracture in linear thin shells. Theoretical and Applied Fracture Mechanics, 2014, 69: 102–109

    Article  Google Scholar 

  13. Areias P, Rabczuk T, Msekh M A. Phase-field analysis of finitestrain plates and shells including element subdivision. Computer Methods in Applied Mechanics and Engineering, 2016, 312: 322–350

    Article  MathSciNet  Google Scholar 

  14. Msekh M A, Silani M, Jamshidian M, Areias P, Zhuang X, Zi G, He P, Rabczuk T. Predictions of J integral and tensile strength of clay/epoxy nanocomposites material using phase field model. Composites. Part B, Engineering, 2016, 93: 97–114

    Article  Google Scholar 

  15. Areias P, Rabczuk T, de Sá J C. A novel two-stage discrete crack method based on the screened poisson equation and local mesh refinement. Computational Mechanics, 2016, 58(6): 1003–1018

    Article  MathSciNet  MATH  Google Scholar 

  16. Areias P, Msekh M A, Rabczuk T. Damage and fracture algorithm using the screened poisson equation and local remeshing. Engineering Fracture Mechanics, 2016, 158: 116–143

    Article  Google Scholar 

  17. Areias P, Reinoso J, Camanho P P, César de Sá J, Rabczuk T. Effective 2D and 3D crack propagation with local mesh refinement and the screened Poisson equation. Engineering Fracture Mechanics, 2018, 189: 339–360

    Article  Google Scholar 

  18. Nguyen V P, Lian H, Rabczuk T, Bordas S. Modelling hydraulic fractures in porous media using flow cohesive interface elements. Engineering Geology, 2017, 225: 68–82

    Article  Google Scholar 

  19. Nguyen B H, Tran H D, Anitescu C, Zhuang X, Rabczuk T. An isogeometric symmetric galerkin boundary element method for twodimensional crack problems. Computer Methods in Applied Mechanics and Engineering, 2016, 306: 252–275

    Article  MathSciNet  Google Scholar 

  20. 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

    Article  MATH  Google Scholar 

  21. 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

    Article  MATH  Google Scholar 

  22. Nanthakumar S, Lahmer T, Zhuang X, Zi G, Rabczuk T. Detection of material interfaces using a regularized level set method in piezoelectric structures. Inverse Problems in Science and Engineering, 2016, 24(1): 153–176

    Article  MathSciNet  Google Scholar 

  23. Bordas S P A, Rabczuk T, Hung N X, Nguyen V P, Natarajan S, Bog T, Quan D M, Hiep N V. Strain smoothing in FEM and XFEM. Computers & Structures, 2010, 88(23–24): 1419–1443

    Article  Google Scholar 

  24. Bordas S P A, Natarajan S, Kerfriden P, Augarde C, Mahapatra D, Rabczuk T, Pont S. On the performance of strain smoothing for quadratic and enriched finite element approximations (XFEM/GFEM/PUFEM). International Journal for Numerical Methods in Engineering, 2011, 86(4–5): 637–666

    Article  MATH  Google Scholar 

  25. Ghorashi S S, Valizadeh N, Mohammadi S, Rabczuk T. T-spline based xiga for fracture analysis of orthotropic media. Computers & Structures, 2015, 147: 138–146

    Article  Google Scholar 

  26. Nguyen-Thanh N, Valizadeh N, Nguyen M N, Nguyen-Xuan H, Zhuang X, Areias P, Zi G, Bazilevs Y, De Lorenzis L, Rabczuk T. An extended isogeometric thin shell analysis based on kirchhofflove theory. Computer Methods in Applied Mechanics and Engineering, 2015, 284: 265–291

    Article  MathSciNet  MATH  Google Scholar 

  27. Chan C L, Anitescu C, Rabczuk T. Volumetric parametrization from a level set boundary representation with pht-splines. Computer Aided Design, 2017, 82: 29–41

    Article  MathSciNet  Google Scholar 

  28. Anitescu C, Jia Y, Zhang Y J, Rabczuk T. An isogeometric collocation method using superconvergent points. Computer Methods in Applied Mechanics and Engineering, 2015, 284: 1073–1097

    Article  MathSciNet  MATH  Google Scholar 

  29. Nguyen V P, Anitescu C, Bordas S P A, Rabczuk T. Isogeometric analysis: an overview and computer implementation aspects. Mathematics and Computers in Simulation, 2015, 117: 89–116

    Article  MathSciNet  Google Scholar 

  30. Ghasemi H, Park H S, Rabczuk T. A level-set based IGA formulation for topology optimization of flexoelectric materials. Computer Methods in Applied Mechanics and Engineering, 2017, 313: 239–258

    Article  MathSciNet  Google Scholar 

  31. Nguyen-Thanh N, Kiendl J, Nguyen-Xuan H, Wüchner R, Bletzinger K U, Bazilevs Y, Rabczuk T. Rotation free isogeometric thin shell analysis using PHT-splines. Computer Methods in Applied Mechanics and Engineering, 2011, 200(47–48): 3410–3424

    Article  MathSciNet  MATH  Google Scholar 

  32. Nguyen-Thanh N, Nguyen-Xuan H, Bordas S P A, Rabczuk T. Isogeometric analysis using polynomial splines over hierarchical Tmeshes for two-dimensional elastic solids. Computer Methods in Applied Mechanics and Engineering, 2011, 200(21–22): 1892–1908

    Article  MathSciNet  MATH  Google Scholar 

  33. Nguyen B H, Tran H D, Anitescu C, Zhuang X, Rabczuk T. An isogeometric symmetric Galerkin boundary element method for two-dimensional crack problems. Computer Methods in Applied Mechanics and Engineering, 2016, 306: 252–275

    Article  MathSciNet  Google Scholar 

  34. Hansbo A, Hansbo P. A finite element method for the simulation of strong and weak discontinuities in solid mechanics. Computer Methods in Applied Mechanics and Engineering, 2004, 193(33–35): 3523–3540

    Article  MathSciNet  MATH  Google Scholar 

  35. Song J H, Areias PMA, Belytschko T. A method for dynamic crack and shear band propagation with phantom nodes. International Journal for Numerical Methods in Engineering, 2006, 67(6): 868–893

    Article  MATH  Google Scholar 

  36. Areias P M A, Song J H, Belytschko T. Analysis of fracture in thin shells by overlapping paired elements. International Journal for Numerical Methods in Engineering, 2006, 195: 5343–5360

    MATH  Google Scholar 

  37. 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

    Article  Google Scholar 

  38. Hamdia K M, Silani M, Zhuang X, He P, Rabczuk T. Stochastic analysis of the fracture toughness of polymeric nanoparticle composites using polynomial chaos expansions. International Journal of Fracture, 2017, 206(2): 215–227

    Article  Google Scholar 

  39. Cai Y, Zhuang X, Zhu H. A generalized and efficient method for finite cover generation in the numerical manifold method. International Journal of Computational Methods, 2013, 10(5): 1350028

    Article  MathSciNet  MATH  Google Scholar 

  40. Nguyen-Xuan H, Liu G R, Bordas S, Natarajan S, Rabczuk T. An adaptive singular ES-FEM for mechanics problems with singular field of arbitrary order. Computer Methods in Applied Mechanics and Engineering, 2013, 253: 252–273

    Article  MathSciNet  MATH  Google Scholar 

  41. Areias PMA, Rabczuk T, Camanho P P. Finite strain fracture of 2D problems with injected anisotropic softening elements. Theoretical and Applied Fracture Mechanics, 2014, 72: 50–63

    Article  Google Scholar 

  42. Areias P, Rabczuk T, Dias da Costa D. Element-wise fracture algorithm based on rotation of edges. Engineering Fracture Mechanics, 2013, 110: 113–137

    Article  Google Scholar 

  43. Areias P, Reinoso J, Camanho P, Rabczuk T. A constitutive-based element-by-element crack propagation algorithm with local mesh refinement. Computational Mechanics, 2015, 56(2): 291–315

    Article  MathSciNet  MATH  Google Scholar 

  44. Areias P, Rabczuk T. Finite strain fracture of plates and shells with configurational forces and edge rotations. International Journal for Numerical Methods in Engineering, 2013, 94(12): 1099–1122

    Article  MathSciNet  MATH  Google Scholar 

  45. Areias P, Rabczuk T. Steiner-point free edge cutting of tetrahedral meshes with applications in fracture. Finite Elements in Analysis and Design, 2017, 132: 27–41

    Article  Google Scholar 

  46. Amiri F, Anitescu C, Arroyo M, Bordas S, Rabczuk T. XLME interpolants, a seamless bridge between XFEM and enriched meshless methods. Computational Mechanics, 2014, 53(1): 45–57

    Article  MathSciNet  MATH  Google Scholar 

  47. Rabczuk T, Areias P M A, Belytschko T. A simplified meshfree method for shear bands with cohesive surfaces. International Journal for Numerical Methods in Engineering, 2007, 69(5): 993–1021

    Article  MATH  Google Scholar 

  48. Rabczuk T, Zi G. A meshfree method based on the local partition of unity for cohesive cracks. Computational Mechanics, 2007, 39(6): 743–760

    Article  MATH  Google Scholar 

  49. Zi G, Rabczuk T, Wall W. Extended meshfree methods without the branch enrichment for cohesive cracks. Computational Mechanics, 2007, 40(2): 367–382

    Article  MATH  Google Scholar 

  50. Rabczuk T, Zi G, Gerstenberger A, Wall W A. A new crack tip element for the phantom node method with arbitrary cohesive cracks. International Journal for Numerical Methods in Engineering, 2008, 75(5): 577–599

    Article  MATH  Google Scholar 

  51. Amiri F, Anitescu C, Arroyo M, Bordas S P A, Rabczuk T. XLME interpolants, a seamless bridge between XFEM and enriched meshless methods. Computational Mechanics, 2014, 53(1): 45–57

    Article  MathSciNet  MATH  Google Scholar 

  52. 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

    Article  Google Scholar 

  53. Rabczuk T, Bordas S, Zi G. A three-dimensional meshfree method for continuous multiple-crack initiation, propagation and junction in statics and dynamics. Computational Mechanics, 2007, 40(3): 473–495

    Article  MATH  Google Scholar 

  54. 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

    MathSciNet  MATH  Google Scholar 

  55. Rabczuk T, Areias P M A, Belytschko T. A meshfree thin shell method for non-linear dynamic fracture. International Journal for Numerical Methods in Engineering, 2007, 72(5): 524–548

    Article  MathSciNet  MATH  Google Scholar 

  56. Rabczuk T, Areias P. A meshfree thin shell for arbitrary evolving cracks based on an extrinsic basis. Computer Modeling in Engineering & Sciences, 2006, 16(2): 115–130

    Google Scholar 

  57. Bordas S, Rabczuk T, Zi G. Three-dimensional crack initiation, propagation, branching and junction in non-linear materials by an extended meshfree method without asymptotic enrichment. Engineering Fracture Mechanics, 2008, 75(5): 943–960

    Article  Google Scholar 

  58. Rabczuk T, Belytschko T, Xiao S P. Stable particle methods based on lagrangian kernels. Computer Methods in Applied Mechanics and Engineering, 2004, 193(12–14): 1035–1063

    Article  MathSciNet  MATH  Google Scholar 

  59. Talebi H, Silani M, Rabczuk T. Concurrent multiscale modelling of three dimensional crack and dislocation propagation. Advances in Engineering Software, 2015, 80: 82–92

    Article  Google Scholar 

  60. 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

    Article  MATH  Google Scholar 

  61. Budarapu P R, Gracie R, Yang S W, Zhuang X, Rabczuk T. Efficient coarse graining in multiscale modeling of fracture. Theoretical and Applied Fracture Mechanics, 2014, 69: 126–143

    Article  Google Scholar 

  62. Budarapu P R, Gracie R, Bordas S P A, Rabczuk T. An adaptive multiscale method for quasi-static crack growth. Computational Mechanics, 2014, 53(6): 1129–1148

    Article  Google Scholar 

  63. Silani M, Talebi H, Hamouda A M, Rabczuk T. Nonlocal damage modelling in clay/epoxy nanocomposites using a multiscale approach. Journal of Computational Science, 2016, 15: 18–23

    Article  Google Scholar 

  64. Talebi H, Silani M, Rabczuk T. Concurrent multiscale modeling of three dimensional crack and dislocation propagation. Advances in Engineering Software, 2015, 80(C): 82–92

    Article  Google Scholar 

  65. Silani M, Talebi H, Ziaei-Rad S, Hamouda A M, Zi G, Rabczuk T. A three dimensional extended Arlequin method for dynamic fracture. Computational Materials Science, 2015, 96(PB): 425–431

    Article  Google Scholar 

  66. Silani M, Ziaei-Rad S, Talebi H, Rabczuk T. A semi-concurrent multiscale approach for modeling damage in nanocomposites. Theoretical and Applied Fracture Mechanics, 2014, 74(1): 30–38

    Article  Google Scholar 

  67. Talebi H, Silani M, Bordas S P A, Kerfriden P, Rabczuk T. A computational library for multiscale modeling of material failure. Computational Mechanics, 2014, 53(5): 1047–1071

    Article  MathSciNet  Google Scholar 

  68. Talebi H, Silani M, Bordas S P A, Kerfriden P, Rabczuk T. Molecular dynamics/XFEM coupling by a three-dimensional extended bridging domain with applications to dynamic brittle fracture. International Journal for Multiscale Computational Engineering, 2013, 11(6): 527–541

    Article  Google Scholar 

  69. Silling S A. Reformulation of elasticity theory for discontinuities and long-range forces. Journal of the Mechanics and Physics of Solids, 2000, 48(1): 175–209

    Article  MathSciNet  MATH  Google Scholar 

  70. Rabczuk T, Ren H. A peridynamics formulation for quasi-static fracture and contact in rock. Engineering Geology, 2017, 225: 42–48

    Article  Google Scholar 

  71. 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

    Article  MathSciNet  Google Scholar 

  72. Ren H, Zhuang X, Cai Y, Rabczuk T. Dual-horizon peridynamics. International Journal for Numerical Methods in Engineering, 2017, 318: 768–782

    Google Scholar 

  73. Rabczuk T, Eibl J. Modelling dynamic failure of concrete with meshfree methods. International Journal of Impact Engineering, 2006, 32(11): 1878–1897

    Article  Google Scholar 

  74. Rabczuk T, Belytschko T. Application of meshfree particle methods to static fracture of reinforced concrete structures. International Journal of Fracture, 2006, 137(1–4): 19–49

    Article  MATH  Google Scholar 

  75. Rabczuk T, Zi G, Bordas S, Nguyen-Xuan H. A geometrically nonlinear three-dimensional cohesive crack method for reinforced concrete structures. Engineering Fracture Mechanics, 2008, 75(16): 4740–4758

    Article  Google Scholar 

  76. Rabczuk T, Akkermann J, Eibl J. A numerical model for reinforced concrete structures. International Journal of Solids and Structures, 2005, 42(5–6): 1327–1354

    Article  MATH  Google Scholar 

  77. Vu-Bac N, Lahmer T, Zhang Y, Zhuang X, Rabczuk T. Stochastic predictions of interfacial characteristic of polymeric nanocomposites (PNCs). Composites Part B: Engineering, 2014, 59: 80–95

    Article  Google Scholar 

  78. Vu-Bac N, Lahmer T, Zhuang X, Nguyen-Thoi T, Rabczuk T. A software framework for probabilistic sensitivity analysis for computationally expensive models. Advances in Engineering Software, 2016, 100: 19–31

    Article  Google Scholar 

  79. Hamdia K, Silani M, Zhuang X, He P, Rabczuk T. Stochastic analysis of the fracture toughness of polymeric nanoparticle composites using polynomial chaos expansions. International Journal of Fracture, 2017, 206(2): 215–227

    Article  Google Scholar 

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The authors acknowledge the support from the Shanghai Municipal Commission of Science and Technology.

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He, P., Shen, Y., Gu, Y. et al. 3D fracture modelling and limit state analysis of prestressed composite concrete pipes. Front. Struct. Civ. Eng. 13, 165–175 (2019). https://doi.org/10.1007/s11709-018-0484-4

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