Numerical simulation of crack propagation in shell structures using interface shell elements


In this study, we present a novel finite element approach to simulate crack propagation in shell structures. A local spider-web mesh is placed at the tip of a crack propagating through a global background mesh. Interface shell elements with assumed natural strains are used to connect a non-matching interface between the background mesh and the local spider-web mesh. Interface shell elements are also employed for trimmed shell elements created by cutting shell elements with the crack line. Numerical simulation of crack propagation in shell structures can be easily performed by moving the local spider-web mesh with an incremental crack growth. Numerical experiments show that the present method is very efficient and effective to accurately simulate crack propagation in shell structures without significantly increasing computational burden and implementation complexity of remeshing process.

This is a preview of subscription content, log in to check access.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18
Fig. 19
Fig. 20
Fig. 21
Fig. 22
Fig. 23
Fig. 24
Fig. 25
Fig. 26
Fig. 27
Fig. 28
Fig. 29
Fig. 30
Fig. 31
Fig. 32


  1. 1.

    Moës N, Dolbow J, Belytschko T (1999) A finite element method for crack growth without remeshing. Int J Numer Methods Eng 46:131–150.;2-J

    MathSciNet  Article  MATH  Google Scholar 

  2. 2.

    Dolbow J, Moës N, Belytschko T (2000) Modeling fracture in Mindlin-Reissner plates with the extended finite element method. Int J Solids Struct 37:7161–7183.

    Article  MATH  Google Scholar 

  3. 3.

    Areias PMA, Belytschko T (2005) Non-linear analysis of shells with arbitrary evolving cracks using XFEM. Int J Numer Methods Eng 62:384–415.

    Article  MATH  Google Scholar 

  4. 4.

    Bayesteh H, Mohammadi S (2011) XFEM fracture analysis of shells: the effect of crack tip enrichments. Comput Mater Sci 50:2793–2813.

    Article  Google Scholar 

  5. 5.

    Larsson R, Mediavilla J, Fagerström M (2011) Dynamic fracture modeling in shell structures based on XFEM. Int J Numer Methods Eng 86:499–527.

    MathSciNet  Article  MATH  Google Scholar 

  6. 6.

    Zeng Q, Liu Z, Xu D et al (2016) Modeling arbitrary crack propagation in coupled shell/solid structures with X-FEM. Int J Numer Methods Eng 106:1018–1040.

    MathSciNet  Article  MATH  Google Scholar 

  7. 7.

    Benson DJ, Bazilevs Y, De Luycker E et al (2010) A generalized finite element formulation for arbitrary basis functions: from isogeometric analysis to XFEM. Int J Numer Methods Eng.

    MathSciNet  Article  MATH  Google Scholar 

  8. 8.

    De Luycker E, Benson DJ, Belytschko T et al (2011) X-FEM in isogeometric analysis for linear fracture mechanics. Int J Numer Methods Eng 87:541–565.

    MathSciNet  Article  MATH  Google Scholar 

  9. 9.

    Ghorashi SS, Valizadeh N, Mohammadi S (2012) Extended isogeometric analysis for simulation of stationary and propagating cracks. Int J Numer Methods Eng 89:1069–1101.

    MathSciNet  Article  MATH  Google Scholar 

  10. 10.

    Nguyen-Thanh N, Valizadeh N, Nguyen MN et al (2015) An extended isogeometric thin shell analysis based on Kirchhoff–Love theory. Comput Methods Appl Mech Eng 284:265–291.

    MathSciNet  Article  MATH  Google Scholar 

  11. 11.

    Areias PMA, Song JH, Belytschko T (2006) Analysis of fracture in thin shells by overlapping paired elements. Comput Methods Appl Mech Eng 195:5343–5360.

    Article  MATH  Google Scholar 

  12. 12.

    Chau-Dinh T, Zi G, Lee P-S et al (2012) Phantom-node method for shell models with arbitrary cracks. Comput Struct 92–93:242–256.

    Article  Google Scholar 

  13. 13.

    Chau-Dinh T, Mai-Van C, Zi G, Rabczuk T (2018) New kinematical constraints of cracked MITC4 shell elements based on the phantom-node method for fracture analysis. Eng Fract Mech 199:159–178.

    Article  Google Scholar 

  14. 14.

    Areias PMA, Belytschko T (2006) A comment on the article “A finite element method for simulation of strong and weak discontinuities in solid mechanics” by A. Hansbo and P. Hansbo [Comput. Methods Appl. Mech. Engrg. 193 (2004) 3523–3540]. Comput Methods Appl Mech Eng 195:1275–1276.

    Article  MATH  Google Scholar 

  15. 15.

    Dirgantara T, Aliabadi MH (2000) Crack growth analysis of plates loaded by bending and tension using dual boundary element method. Int J Fract 105:27–47.

    Article  Google Scholar 

  16. 16.

    Dirgantara T, Aliabadi MH (2002) Numerical simulation of fatigue crack growth in pressurized shells. Int J Fatigue 24:725–738.

    Article  MATH  Google Scholar 

  17. 17.

    Xing C, Zhou C (2018) Finite element modeling of crack growth in thin-wall structures by method of combining sub-partition and substructure. Eng Fract Mech 195:13–29.

    Article  Google Scholar 

  18. 18.

    Bouchard PO, Bay F, Chastel Y, Tovena I (2000) Crack propagation modelling using an advanced remeshing technique. Comput Methods Appl Mech Eng 189:723–742.

    Article  MATH  Google Scholar 

  19. 19.

    Bouchard PO, Bay F, Chastel Y (2003) Numerical modelling of crack propagation: automatic remeshing and comparison of different criteria. Comput Methods Appl Mech Eng 192:3887–3908.

    Article  MATH  Google Scholar 

  20. 20.

    Funari MF, Lonetti P, Spadea S (2019) A crack growth strategy based on moving mesh method and fracture mechanics. Theor Appl Fract Mech 102:103–115.

    Article  Google Scholar 

  21. 21.

    Murotani K, Yagawa G, Choi JB (2013) Adaptive finite elements using hierarchical mesh and its application to crack propagation analysis. Comput Methods Appl Mech Eng 253:1–14.

    MathSciNet  Article  MATH  Google Scholar 

  22. 22.

    Ooi ET, Man H, Natarajan S, Song C (2015) Adaptation of quadtree meshes in the scaled boundary finite element method for crack propagation modelling. Eng Fract Mech 144:101–117.

    Article  Google Scholar 

  23. 23.

    Khoei AR, Azadi H, Moslemi H (2008) Modeling of crack propagation via an automatic adaptive mesh refinement based on modified superconvergent patch recovery technique. Eng Fract Mech 75:2921–2945.

    Article  Google Scholar 

  24. 24.

    Colombo D, Giglio M (2006) A methodology for automatic crack propagation modelling in planar and shell FE models. Eng Fract Mech 73:490–504.

    Article  Google Scholar 

  25. 25.

    Nguyen-Thanh N, Li W, Zhou K (2018) Static and free-vibration analyses of cracks in thin-shell structures based on an isogeometric-meshfree coupling approach. Comput Mech 62:1287–1309.

    MathSciNet  Article  MATH  Google Scholar 

  26. 26.

    Rashid MM (1998) The arbitrary local mesh replacement method: an alternative to remeshing for crack propagation analysis. Comput Methods Appl Mech Eng 154:133–150.

    Article  MATH  Google Scholar 

  27. 27.

    Kim H-G (2002) Interface element method (IEM) for a partitioned system with non-matching interfaces. Comput Methods Appl Mech Eng 191:3165–3194.

    MathSciNet  Article  MATH  Google Scholar 

  28. 28.

    Kim H-G (2003) Arbitrary placement of local meshes in a global mesh by the interface-element method (IEM). Int J Numer Methods Eng 56:2279–2312.

    Article  MATH  Google Scholar 

  29. 29.

    Ho-Nguyen-Tan T, Kim H-G (2018) An interface shell element for coupling non-matching quadrilateral shell meshes. Comput Struct 208:151–173.

    Article  Google Scholar 

  30. 30.

    Lim JH, Im S, Cho Y-S (2007) Variable-node elements for non-matching meshes by means of MLS (moving least-square) scheme. Int J Numer Methods Eng 72:835–857.

    Article  MATH  Google Scholar 

  31. 31.

    Cho Y-S, Im S (2006) MLS-based variable-node elements compatible with quadratic interpolation. Part II: application for finite crack element. Int J Numer Methods Eng 65:517–547.

    Article  MATH  Google Scholar 

  32. 32.

    Bathe K-J (1996) Finite element procedures, 2nd edn. Prentice Hall, Upper Saddle River

    Google Scholar 

  33. 33.

    Sohn D, Im S (2013) Variable-node plate and shell elements with assumed natural strain and smoothed integration methods for nonmatching meshes. Comput Mech 51:927–948.

    Article  MATH  Google Scholar 

  34. 34.

    Hou Cheng Huang (1987) Implementation of assumed strain degenerated shell elements. Comput Struct 25:147–155.

    Article  MATH  Google Scholar 

  35. 35.

    Ko Y, Lee P-S, Bathe K-J (2017) A new MITC4 + shell element. Comput Struct 182:404–418.

    Article  Google Scholar 

  36. 36.

    Ko Y, Lee P-S, Bathe K-J (2016) The MITC4 + shell element and its performance. Comput Struct 169:57–68.

    Article  Google Scholar 

  37. 37.

    Stern M, Becker EB, Dunham RS (1976) A contour integral computation of mixed-mode stress intensity factors. Int J Fract 12:359–368.

    Article  Google Scholar 

  38. 38.

    Yau JF, Wang SS, Corten HT (1980) A mixed-mode crack analysis of isotropic solids using conservation laws of elasticity. J Appl Mech 47:335–341.

    Article  MATH  Google Scholar 

  39. 39.

    Nikishkov GP, Atluri SN (1987) Calculation of fracture mechanics parameters for an arbitrary three-dimensional crack, by the ‘equivalent domain integral’ method. Int J Numer Methods Eng 24:1801–1821.

    Article  MATH  Google Scholar 

  40. 40.

    Zehnder AT, Viz MJ (2005) Fracture mechanics of thin plates and shells under combined membrane, bending, and twisting loads. Appl Mech Rev 58:37–48.

    Article  Google Scholar 

  41. 41.

    Potyondy DO, Wawrzynek PA, Ingraffea AR (1995) Discrete crack growth analysis methodology for through cracks in pressurized fuselage structures. Int J Numer Methods Eng 38:1611–1633.

    Article  MATH  Google Scholar 

  42. 42.

    Erdogan F, Sih GC (1963) On the crack extension in plates under plane loading and transverse shear. J Basic Eng 85:519–525.

    Article  Google Scholar 

  43. 43.

    Sih GC (1974) Strain-energy-density factor applied to mixed mode crack problems. Int J Fract 10:305–321.

    Article  Google Scholar 

  44. 44.

    Nuismer RJ (1975) An energy release rate criterion for mixed mode fracture. Int J Fract 11:245–250.

    Article  Google Scholar 

  45. 45.

    Lee P-S, Bathe K-J (2004) Development of MITC isotropic triangular shell finite elements. Comput Struct 82:945–962.

    Article  Google Scholar 

  46. 46.

    Sosa HA, Eischen JW (1986) Computation of stress intensity factors for plate bending via a path-independent integral. Eng Fract Mech 25:451–462.

    Article  Google Scholar 

  47. 47.

    Folias ES (1969) On the effect of initial curvature on cracked flat sheets. Int J Fract Mech 5:327–346.

    Article  Google Scholar 

Download references


This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (No. 2018R1A2B6006234).

Author information



Corresponding author

Correspondence to Hyun-Gyu Kim.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Ho-Nguyen-Tan, T., Kim, H. Numerical simulation of crack propagation in shell structures using interface shell elements. Comput Mech (2020).

Download citation


  • Crack propagation
  • Non-matching interface
  • Interface shell elements
  • Assumed natural strains
  • Transverse shear locking
  • Membrane locking