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Modeling crack in viscoelastic media using the extended finite element method

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Abstract

In this paper, the problem of modeling crack in 2D viscoelastic media is studied using the extended finite element method. The paper focuses on the definition of enrichment functions suitable for cracks assessment in viscoelastic media and the generalized domain integrals used in the determination of crack tip parameters. The opening mode and mixed mode solutions of crack tip fracture problems in viscoelastic media are also undertaken. The results obtained by the proposed method show good agreement with the analytical methods and provide reasonable background information to enhance the modeling of crack growth in viscoelastic media.

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References

  1. Schapery R A A. Theory of crack initiation and growth in viscoelastic media. I. Theoretical development. Int J Fract, 1975, 11: 141–159

    Article  Google Scholar 

  2. Schapery R A A. Theory of crack initiation and growth in viscoelastic media. II. Approximate methods of analysis. Int J Fract, 1975, 11: 369–388

    Google Scholar 

  3. Claude C, Frédéric D. A new incremental formulation in the time domain for crack initiation in an orthotropic linearly viscoelastic solid. Mech Time-Dependent Mater, 2001, 5: 229–253

    Article  Google Scholar 

  4. Belytschko T, Black T. Elastic crack growth in finite elements with minimal remeshing. Int J Numer Meth Eng, 1999, 45: 601–620

    Article  MathSciNet  MATH  Google Scholar 

  5. Melenk J M, Babuška I. The partition of unity finite element method: Basic theory and applications. Comput Meth Appl Mech Eng, 1996, 139: 289–314

    Article  MATH  Google Scholar 

  6. Duarte C A, Oden J T. An H-p adaptive method using clouds. Comput Meth Appl Mech Eng, 1996, 139: 237–262

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MATH  Google Scholar 

  8. Cox J V. An extended finite element method with analytical enrichment for cohesive crack modeling. Internat J Numer Methods Engrg, 2009, 78: 48–84

    Article  MathSciNet  MATH  Google Scholar 

  9. Sukumar N, Prévost J H. Modeling quasi-static crack growth with the extended finite element method. Part I: Computer implementation. Int J Solids Struct, 2003, 40: 7513–7537

    Article  MATH  Google Scholar 

  10. Sukumar N, Chopp D L, Moran B. Extended finite element method and fast marching method for three-dimensional fatigue crack propagation. Eng Fract Mech, 2003, 70: 29–48

    Article  Google Scholar 

  11. Sukumar N, Huang Z Y, Prévost J H, et al. Partition of unity enrichment for bimaterial interface cracks. Int J Numer Meth Engng, 2004, 59: 1075–1102

    Article  MATH  Google Scholar 

  12. Combescure A, Gravouil A, Gregoire D, et al. X-FEM a good candidate for energy conservation in simulation of brittle dynamic crack propagation. Comput Meth Appl Mech Eng, 2008, 197: 309–318

    Article  MATH  Google Scholar 

  13. Karihaloo B L, Xiao Q Z. Modelling of stationary and growing cracks in FE framework without remeshing: A state-of-the-art review. Comput Struct, 2003, 81: 119–129

    Article  Google Scholar 

  14. Abdelaziz Y, Hamouine A. A survey of the extended finite element. Comput Struct, 2008, 86: 1141–1151

    Article  Google Scholar 

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

    Article  Google Scholar 

  16. Fries T P, Belytschko T. The extended/generalized finite element method: An overview of the method and its applications. Int J Numer Meth Engng, 2010, DOI: 10.1002/nme.2914

  17. Khoei A R, Shamloo A, Azami A R. Extended finite element method in plasticity forming of powder compaction with contact friction. Int J Solids Struct, 2006, 43: 5421–5448

    Article  MATH  Google Scholar 

  18. Khoei A R, Nikbakht M. An enriched finite element algorithm for numerical computation of contact friction problems. Int J Mech Sci, 2007, 49: 183–199

    Article  Google Scholar 

  19. Prabel B, Combescure A, Gravouil A, et al. Level set X-FEM non-matching meshes: Application to dynamic crack propagation in elasto-plastic media. Int J Numer Meth Engng, 2006, 69: 1553–1569

    Article  Google Scholar 

  20. Elguedj T, Gravouil A, Combescure A. A mixed augmented Lagrangian-extended finite element method for modeling elastic-plastic fatigue crack growth with unilateral contact. Int J Numer Meth Engng, 2007, 71: 1569–1597

    Article  MathSciNet  MATH  Google Scholar 

  21. Anahid M, Khoei A R. New development in extended finite element modeling of large elasto-plastic deformations. Int J Numer Meth Engng, 2008, 75: 1133–1171

    Article  MathSciNet  MATH  Google Scholar 

  22. Zhang H H, Li L X. Modeling inclusion problems in viscoelastic materials with the extended finite element method. Finite Elem Anal Design, 2009, 45: 721–729

    Article  Google Scholar 

  23. Zhang C Y. Vicoelastic Fracture Mechanics. Beijing: Science Press, 2006

    Google Scholar 

  24. Béchet E, Minnebo H, Moës N, et al. Improved implementation and robustness study of the X-FEM for stress analysis around cracks. Int J Numer Meth Engng, 2005, 64: 1033–1056

    Article  MATH  Google Scholar 

  25. Liu X Y, Xiao Q Z, Karihaloo B L. XFEM for direct evaluation of mixed mode SIFs in homogeneous and bi-materials. Int J Numer Meth Eng, 2004, 59: 1103–1118

    Article  MATH  Google Scholar 

  26. Chessa J, Wang H, Belytschko T. On the construction of blending elements for local partition of unity enriched finite elements. Int J Numer Meth Engng, 2003, 57: 1015–1038

    Article  MATH  Google Scholar 

  27. Sukumar N, Chopp D L, Moës N, et al. Modeling holes and inclusions by level sets in the extended finite-element method. Comput Meth Appl Mech Eng, 2001, 190: 6183–6200

    Article  MATH  Google Scholar 

  28. Tarancón J E, Vercher A, Giner E, et al. Enhanced blending elements for XFEM applied to linear elastic fracture mechanics. Int J Numer Meth Engng, 2009, 77: 126–148

    Article  MATH  Google Scholar 

  29. Chessa J. The Extended XFEM for Free Surface and Two Phase Flow Problems. Dissertation of Doctoral Degree. Chicago: Northwestern University, USA, 2003

    Google Scholar 

  30. Gracie R, Wang H, Belytschko T. Blending in the extended finite element method by discontinuous Galerkin and assumed strain methods. Int J Numer Meth Engng, 2008, 74: 1645–1669

    Article  MathSciNet  MATH  Google Scholar 

  31. Fries T P. A corrected XFEM approximation without problems in blending elements. Int J Numer Meth Engng, 2008, 75: 503–532

    Article  MathSciNet  MATH  Google Scholar 

  32. Shibanuma K, Utsunomiya T. Reformulation of XFEM based on PUFEM for solving problem caused by blending elements. Finite Elem Anal Design, 2009, 45: 806–816

    Article  MathSciNet  Google Scholar 

  33. Natarajan S, Bordas S, Mahapatra D R. Numerical integration over arbitrary polygonal domains based on Schwarz-Christoffel conformal mapping. Int J Numer Meth Engng, 2009, 80: 103–134

    Article  MathSciNet  MATH  Google Scholar 

  34. Natarajan S, Mahapatra D R, Bordas S. Integrating strong and weak discontinuities without integration subcells and example applications in an XFEM/GFEM framework. Int J Numer Meth Engng, 2010, DOI: 10.1002/nme.2798

  35. Bordas S, Nguyen P V, Dunant C, et al. An extended finite element library. Int J Numer Meth Engng, 2006, 2: 1–33

    Google Scholar 

  36. Tada H, Paris P C, Irwin R. The stress analysis of cracks, Handbook. Del Research Corporation, Hellertown, Pennsylvania, 1973

    Google Scholar 

  37. Zhang C Y. On the time-dependent G i-K i relationships for viscoelastic cracked bodies (in Chinese). J Xiangtan Univ, 1980, (2): 110–125

    Google Scholar 

  38. Wilson W K. Combined Mode Fracture Mechanics. Dissertation of Doctoral Degree. Pittsburgh: University of Pittsburgh, USA, 1969

    Google Scholar 

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Yu, T., Ren, Q. Modeling crack in viscoelastic media using the extended finite element method. Sci. China Technol. Sci. 54, 1599–1606 (2011). https://doi.org/10.1007/s11431-010-4283-y

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  • DOI: https://doi.org/10.1007/s11431-010-4283-y

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