Skip to main content
SpringerLink
Log in

A conforming to interface structured adaptive mesh refinement technique for modeling fracture problems

  • Original Paper
  • Published:
Computational Mechanics Aims and scope Submit manuscript

Abstract

A Conforming to Interface Structured Adaptive Mesh Refinement (CISAMR) technique is introduced for the automated transformation of a structured grid into a conforming mesh with appropriate element aspect ratios. The CISAMR algorithm is composed of three main phases: (i) Structured Adaptive Mesh Refinement (SAMR) of the background grid; (ii) r-adaptivity of the nodes of elements cut by the crack; (iii) sub-triangulation of the elements deformed during the r-adaptivity process and those with hanging nodes generated during the SAMR process. The required considerations for the treatment of crack tips and branching cracks are also discussed in this manuscript. Regardless of the complexity of the problem geometry and without using iterative smoothing or optimization techniques, CISAMR ensures that aspect ratios of conforming elements are lower than three. Multiple numerical examples are presented to demonstrate the application of CISAMR for modeling linear elastic fracture problems with intricate morphologies.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

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

Similar content being viewed by others

References

  1. Camacho GT, Ortiz M (1996) Computational modelling of impact damage in brittle materials. Int J Solids Struct 33(20):2899–2938

    Article  MATH  Google Scholar 

  2. Bouchard PO, Bay F, Chastel Y, Tovena I (2000) Crack propagation modelling using an advanced remeshing technique. Comput Methods Appl Mech Eng 189(3):723–742

    Article  MATH  Google Scholar 

  3. Colombo D, Giglio M (2006) A methodology for automatic crack propagation modelling in planar and shell FE models. Eng Fract Mech 73(4):490–504

    Article  Google Scholar 

  4. Nishioka T, Tokudome H, Kinoshita M (2001) Dynamic fracture-path prediction in impact fracture phenomena using moving finite element method based on Delaunay automatic mesh generation. Int J Solids Struct 38(30):5273–5301

    Article  MATH  Google Scholar 

  5. Azócar D, Elgueta M, Rivara MC (2010) Automatic LEFM crack propagation method based on local Lepp–Delaunay mesh refinement. Adv Eng Softw 41(2):111–119

    Article  MATH  Google Scholar 

  6. 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(10):2921–2945

    Article  Google Scholar 

  7. Meyer A, Rabold F, Scherzer M (2006) Efficient finite element simulation of crack propagation using adaptive iterative solvers. Commun Numer Methods Eng 22(2):93–108

    Article  MathSciNet  MATH  Google Scholar 

  8. Askes H, Sluys LJ, de Jong BBC (2000) Remeshing techniques for r-adaptive and combined h/r-adaptive analysis with application to 2D/3D crack propagation. In: European Congress on Computational Methods in Applied Sciences and Engineering, ECCOMAS

  9. Areias P, Rabczuk T (2013) Finite strain fracture of plates and shells with configurational forces and edge rotations. Int J Numer Methods Eng 94(12):1099–1122

    Article  MathSciNet  MATH  Google Scholar 

  10. Areias P, Rabczuk T, Camanho PP (2013) Initially rigid cohesive laws and fracture based on edge rotations. Comput Mech 52(4):931–947

    Article  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  12. Areias P, Msekh MA, Rabczuk T (2016) Damage and fracture algorithm using the screened poisson equation and local remeshing. Eng Fract Mech 158:116–143

    Article  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  14. Rangarajan R, Chiaramonte MM, Hunsweck MJ, Shen Y, Lew AJ (2015) Simulating curvilinear crack propagation in two dimensions with universal meshes. Int J Numer Methods Eng 102(3–4):632–670

    Article  MathSciNet  MATH  Google Scholar 

  15. Henshell RD, Shaw KG (1975) Crack tip finite elements are unnecessary. Int J Numer Methods Eng 9(3):495–507

    Article  MATH  Google Scholar 

  16. Barsoum RS (1976) On the use of isoparametric finite elements in linear fracture mechanics. Int J Numer Methods Eng 10(1):25–37

    Article  MATH  Google Scholar 

  17. Rashid MM (1998) The arbitrary local mesh replacement method: an alternative to remeshing for crack propagation analysis. Comput Methods Appl Mech Eng 154(1):133–150

    Article  MATH  Google Scholar 

  18. Xu XP, Needleman A (1994) Numerical simulations of fast crack growth in brittle solids. J Mech Phys Solids 42(9):1397–1434

    Article  MATH  Google Scholar 

  19. Zhang Z, Paulino GH, Celes W (2008) Cohesive modeling of dynamic crack growth in homogeneous and functionally graded materials. Multiscale Funct Grad Mater 973:562–567

    Google Scholar 

  20. Jin ZH, Paulino GH, Dodds RH (2002) Finite element investigation of quasi-static crack growth in functionally graded materials using a novel cohesive zone fracture model. J Appl Mech 69(3):370–379

    Article  MATH  Google Scholar 

  21. Zhang ZJ, Paulino GH, Celes W (2007) Extrinsic cohesive modelling of dynamic fracture and microbranching instability in brittle materials. Int J Numer Methods Eng 72(8):893–923

    Article  MATH  Google Scholar 

  22. Park K, Paulino GH, Celes W, Espinha R (2012) Adaptive mesh refinement and coarsening for cohesive zone modeling of dynamic fracture. Int J Numer Methods Eng 92(1):1–35

    Article  MathSciNet  MATH  Google Scholar 

  23. Nguyen VP (2014) An open source program to generate zero-thickness cohesive interface elements. Adv Eng Softw 74:27–39

    Article  Google Scholar 

  24. Li S, Liu WK (2002) Meshfree and particle methods and their applications. Appl Mech Rev 55(1):1–34

    Article  Google Scholar 

  25. Belytschko T, Lu YY, Gu L (1994) Element-free Galerkin methods. Int J Numer Methods Eng 37(2):229–256

    Article  MathSciNet  MATH  Google Scholar 

  26. Belytschko T, Gu L, Lu YY (1994) Fracture and crack growth by element free Galerkin methods. Modell Simul Mater Sci Eng 2(3A):519

    Article  Google Scholar 

  27. Belytschko T, Lu YY, Gu L, Tabbara M (1995) Element-free Galerkin methods for static and dynamic fracture. Int J Solids Struct 32(17):2547–2570

    Article  MATH  Google Scholar 

  28. Rabczuk T, Belytschko T (2005) Adaptivity for structured meshfree particle methods in 2D and 3D. Int J Numer Methods Eng 63(11):1559–1582

    Article  MathSciNet  MATH  Google Scholar 

  29. Rabczuk T, Samaniego E (2008) Discontinuous modelling of shear bands using adaptive meshfree methods. Comput Methods Appl Mech Eng 197(6):641–658

    Article  MathSciNet  MATH  Google Scholar 

  30. Liu WK, Hao S, Belytschko T, Li S, Chang CT (1999) Multiple scale meshfree methods for damage fracture and localization. Comput Mater Sci 16(1):197–205

    Article  Google Scholar 

  31. Rabczuk T, Belytschko T (2004) Cracking particles: a simplified meshfree method for arbitrary evolving cracks. Int J Numer Methods Eng 61(13):2316–2343

    Article  MATH  Google Scholar 

  32. Silling SA, Askari E (2005) A meshfree method based on the peridynamic model of solid mechanics. Comput Struct 83(17):1526–1535

    Article  Google Scholar 

  33. Silling SA, Epton M, Weckner O, Xu J, Askari E (2007) Peridynamic states and constitutive modeling. J Elast 88(2):151–184

    Article  MathSciNet  MATH  Google Scholar 

  34. Hu W, Ha YD, Bobaru F (2012) Peridynamic model for dynamic fracture in unidirectional fiber-reinforced composites. Comput Methods Appl Mech Eng 217:247–261

    Article  MathSciNet  MATH  Google Scholar 

  35. Ha YD, Bobaru F (2011) Characteristics of dynamic brittle fracture captured with peridynamics. Eng Fract Mech 78(6):1156–1168

    Article  Google Scholar 

  36. Breitenfeld MS, Geubelle PH, Weckner O, Silling SA (2014) Non-ordinary state-based peridynamic analysis of stationary crack problems. Comput Methods Appl Mech Eng 272:233–250

    Article  MathSciNet  MATH  Google Scholar 

  37. Karma A, Kessler DA, Levine H (2001) Phase-field model of mode III dynamic fracture. Phys Rev Lett 87(4):045501

    Article  Google Scholar 

  38. Miehe C, Welschinger F, Hofacker M (2010) Thermodynamically consistent phase-field models of fracture: variational principles and multi-field FE implementations. Int J Numer Methods Eng 83(10):1273–1311

    Article  MathSciNet  MATH  Google Scholar 

  39. Hofacker M, Miehe C (2013) A phase field model of dynamic fracture: Robust field updates for the analysis of complex crack patterns. Int J Numer Methods Eng 93(3):276–301

    Article  MathSciNet  MATH  Google Scholar 

  40. Borden MJ, Verhoosel CV, Scott MA, Hughes TJ, Landis CM (2012) A phase-field description of dynamic brittle fracture. Comput Methods Appl Mech Eng 217:77–95

    Article  MathSciNet  MATH  Google Scholar 

  41. Welschinger F, Hofacker M, Miehe C (2010) Configurational-force-based adaptive FE solver for a phase field model of fracture. PAMM 10(1):689–692

    Article  MATH  Google Scholar 

  42. Heister T, Wheeler MF, Wick T (2015) A primal-dual active set method and predictor-corrector mesh adaptivity for computing fracture propagation using a phase-field approach. Comput Methods Appl Mech Eng 290:466–495

    Article  MathSciNet  Google Scholar 

  43. Wells GN, Sluys LJ (2001) A new method for modelling cohesive cracks using finite elements. Int J Numer Methods Eng 50(12):2667–2682

    Article  MATH  Google Scholar 

  44. Armero F, Linder C (2008) New finite elements with embedded strong discontinuities in the finite deformation range. Comput Methods Appl Mech Eng 197(33):3138–3170

    Article  MathSciNet  MATH  Google Scholar 

  45. Armero F, Linder C (2009) Numerical simulation of dynamic fracture using finite elements with embedded discontinuities. Int J Fract 160(2):119–141

    Article  MATH  Google Scholar 

  46. Linder C, Armero F (2007) Finite elements with embedded strong discontinuities for the modeling of failure in solids. Int J Numer Methods Eng 72(12):1391–1433

    Article  MathSciNet  MATH  Google Scholar 

  47. Babuska I, Melenk JM (1997) The partition of unity method. Int J Numer Methods Eng 40(4):727–758

    Article  MathSciNet  MATH  Google Scholar 

  48. Simone A, Duarte CA, Van der Giessen E (2006) A generalized finite element method for polycrystals with discontinuous grain boundaries. Int J Numer Methods Eng 67(8):1122–1145

    Article  MathSciNet  MATH  Google Scholar 

  49. Duddu R, Bordas S, Chopp D, Moran B (2008) A combined extended finite element and level set method for biofilm growth. Int J Numer Methods Eng 74(5):848–870

    Article  MathSciNet  MATH  Google Scholar 

  50. Dolbow J, Moës N, Belytschko T (2001) An extended finite element method for modeling crack growth with frictional contact. Comput Methods Appl Mech Eng 190(51):6825–6846

    Article  MathSciNet  MATH  Google Scholar 

  51. Melenk JM, Babuska I (1996) The partition of unity finite element method: basic theory and applications. Comput Methods Appl Mech Eng 139(1–4):289–314

    Article  MathSciNet  MATH  Google Scholar 

  52. Chessa J, Wang H, Belytschko T (2003) On the construction of blending elements for local partition of unity enriched finite elements. Int J Numer Methods Eng 57:1015–1038

    Article  MATH  Google Scholar 

  53. Fries TP (2008) A corrected XFEM approximation without problems in blending elements. Int J Numer Methods Eng 75(5):503–532

    Article  MathSciNet  MATH  Google Scholar 

  54. Zi G, Belytschko T (2003) New crack-tip elements for XFEM and applications to cohesive cracks. Int J Numer Methods Eng 57(15):2221–2240

    Article  MATH  Google Scholar 

  55. Chahine E, Laborde P, Renard Y (2008) Crack tip enrichment in the XFEM using a cutoff function. Int J Numer Methods Eng 75(6):629–646

    Article  MathSciNet  MATH  Google Scholar 

  56. Song JH, Wang H, Belytschko T (2008) A comparative study on finite element methods for dynamic fracture. Comput Mech 42(2):239–250

    Article  MATH  Google Scholar 

  57. Byfut A, Schroöder A (2012) hp-adaptive extended finite element method. Int J Numer Methods Eng 89(11):1392–1418

    Article  MathSciNet  MATH  Google Scholar 

  58. Fries TP, Byfut A, Alizada A, Cheng KW, Schroöder A (2011) Hanging nodes and XFEM. Int J Numer Methods Eng 86(4–5):404–430

    Article  MathSciNet  MATH  Google Scholar 

  59. Oden TJ, Duarte CA, Zienkiewicz OC (1998) A new cloud-based hp finite element method. Comput Methods Appl Mech Eng 153(1–2):117–126

    Article  MathSciNet  MATH  Google Scholar 

  60. Moës N, Belytschko T (2002) Extended finite element method for cohesive crack growth. Eng Fract Mech 69:813–833

    Article  Google Scholar 

  61. Karoui A, Mansouri K, Renard Y, Arfaoui M (2014) The extended finite element method for cracked hyperelastic materials: a convergence study. Int J Numer Methods Eng 100(3):222–242

    Article  MathSciNet  MATH  Google Scholar 

  62. Nicaise S, Renard Y, Chahine E (2011) Optimal convergence analysis for the extended finite element method. Int J Numer Methods Eng 86(4–5):528–548

    Article  MathSciNet  MATH  Google Scholar 

  63. Belytschko T, Gracie R, Ventura G (2009) A review of extended/generalized finite element methods for material modeling. Modell Simul Mater Sci Eng 17(4):043001

    Article  Google Scholar 

  64. Lang C, Makhija D, Doostan A, Maute K (2014) A simple and efficient preconditioning scheme for heaviside enriched xfem. Comput Mech 54(5):1357–1374

    Article  MathSciNet  MATH  Google Scholar 

  65. Chessa J, Belytschko T (2003) An enriched finite element method and level sets for axisymetric two-phase flow with surface tension. Int J Numer Methods Eng 58:2041–2064

    Article  MATH  Google Scholar 

  66. Piegl L, Tiller W (2012) The NURBS book. Springer, Berlin

    MATH  Google Scholar 

  67. Baase S (2009) Computer algorithms: introduction to design and analysis. Pearson Education, India, Bangalore

    MATH  Google Scholar 

  68. Demkowicz L (2007) Computing with hp-adaptive finite elements. Vol. 1: One- and two-dimensional elliptic and Maxwell problems. CRC Applied Mathematics and Nonlinear Science Series. Chapman and Hall

  69. Anderson TL, Anderson TL (2005) Fracture mechanics: fundamentals and applications. CRC Press, Boca Raton

    MATH  Google Scholar 

  70. Zienkiewicz OC, Taylor RL, Zhu JZ (2005) The finite element method: its basis and fundamentals. Elsevier, Amsterdam

    MATH  Google Scholar 

  71. Dietzel W, Turnbull A (2007) Stress corrosion cracking. GKSS-Forschungszentrum, Bibliothek

Download references

Acknowledgements

This article is based upon work supported by the National Science Foundation under Grant No. 1608058.

Author information

Authors and Affiliations

  1. Department of Mechanical and Aerospace Engineering, The Ohio State University, 201 West 19th Avenue, Columbus, OH, USA

    Soheil Soghrati, Fei Xiao & Anand Nagarajan

  2. Department of Materials Science and Engineering, The Ohio State University, 2041 N. College Road, Columbus, OH, USA

    Soheil Soghrati

Authors
  1. Soheil Soghrati
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Fei Xiao
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Anand Nagarajan
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Soheil Soghrati.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Soghrati, S., Xiao, F. & Nagarajan, A. A conforming to interface structured adaptive mesh refinement technique for modeling fracture problems. Comput Mech 59, 667–684 (2017). https://doi.org/10.1007/s00466-016-1366-z

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00466-016-1366-z

Keywords

Search

Navigation