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3D Dynamic Crack Propagation by the Extended Finite Element Method and a Gradient-Enhanced Damage Model

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Multiscale Modeling of Heterogeneous Structures

Part of the book series: Lecture Notes in Applied and Computational Mechanics ((LNACM,volume 86))

Abstract

A combined continuous-discontinuous approach to fracture is presented to model crack propagation under dynamic loading. A gradient-enhanced damage model is used to evaluate degradation of the material ahead of the crack. This type of model avoids mesh dependency and pathological effects of local damage models. Discrete cracks are reflected by means of extended finite elements (XFEM) and level sets. For the transition between damage and discrete fracture a damage based criterion is utilized. A discrete crack propagates if a critical damage value at the crack front is reached. The propagation direction is also determined through the damage field. Finally a dynamic mode II crack propagation example is simulated to show the capabilities and robustness of the employed approach.

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References

  1. Martha, L.F., Wawrzynek, P.A., Ingraffea, A.R.: Arbitrary crack representation using solid modeling. Eng. Comput. 9(2), 63–82 (1993)

    Article  Google Scholar 

  2. Potyondy, D.O., Wawrzynek, P.A., Ingraffea, A.R.: An algorithm to generate quadrilateral or triangular element surface meshes in arbitrary domains with applications to crack propagation. Int. J. Numer. Methods Eng. 38(16), 2677–2701 (1995)

    Article  MATH  Google Scholar 

  3. Belytschko, T., Chen, H., Xu, J., Zi, G.: Dynamic crack propagation based on loss of hyperbolicity and a new discontinuous enrichment. Int. J. Numer. Methods Eng. 58(12), 1873–1905 (2003)

    Article  MATH  Google Scholar 

  4. Camacho, G., Ortiz, M.: Computational modelling of impact damage in brittle materials. Int. J. Solids Struct. 33(20–22), 2899–2938 (1996)

    Article  MATH  Google Scholar 

  5. Song, J.H., Areias, P.M.A., Belytschko, T.: A method for dynamic crack and shear band propagation with phantom nodes. Int. J. Numer. Methods Eng. 67(6), 868–893 (2006)

    Article  MATH  Google Scholar 

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

    Article  MATH  Google Scholar 

  7. Belytschko, T., Fish, J., Engelmann, B.E.: A finite element with embedded localization zones. Comput. Methods Appl. Mech. Eng. 70(1), 59–89 (1988)

    Article  MATH  Google Scholar 

  8. Lloberas-Valls, O., Huespe, A., Oliver, J., Dias, I.: Strain injection techniques in dynamic fracture modeling. Comput. Methods Appl. Mech. Eng. 308, 499–534 (2016)

    Article  MathSciNet  Google Scholar 

  9. Silling, S.: Dynamic fracture modeling with a meshfree peridynamic code. Comput. Fluid Solid Mech. 2003, 641–644 (2003)

    Google Scholar 

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

    Article  Google Scholar 

  11. Belytschko, T., Organ, D., Gerlach, C.: Element-free galerkin methods for dynamic fracture in concrete. Comput. Methods Appl. Mech. Eng. 187(3–4), 385–399 (2000)

    Article  MATH  Google Scholar 

  12. Raymond, S., Lemiale, V., Ibrahim, R., Lau, R.: A meshfree study of the Kalthoffwinkler experiment in 3D at room and low temperatures under dynamic loading using viscoplastic modelling. Eng. Anal. Boundary Elem. 42, 20–25 (2014)

    Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  14. Moes, N., Dolbow, J., Belytschko, T.: A finite element method for crack growth without remeshing. Int. J. Numer. Methods Eng. 46(1), 131–150 (1999)

    Article  MATH  Google Scholar 

  15. Moës, N., Gravouil, A., Belytschko, T.: Non-planar 3D crack growth by the extended finite element and level sets-part I: mechanical model. Int. J. Numer. Methods Eng. 53(11), 2549–2568 (2002)

    Article  MATH  Google Scholar 

  16. Stolarska, M., Chopp, D.L., Moës, N., Belytschko, T.: Modelling crack growth by level sets in the extended finite element method. Int. J. Numer. Methods Eng. 51(8), 943–960 (2001)

    Article  MATH  Google Scholar 

  17. Strouboulis, T., Babuška, I., Copps, K.: The design and analysis of the generalized finite element method. Comput. Methods Appl. Mech. Eng. 181, 43–69 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  18. Strouboulis, T., Copps, K., Babuška, I.: The generalized finite element method. Comput. Methods Appl. Mech. Eng. 190, 4081–4193 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  19. Pijaudier-Cabot, G., Baẑant, Z.P.: Nonlocal damage theory. J. Eng. Mech. 113(0), 1512–1533 (1987)

    Google Scholar 

  20. Peerlings, R.H.J., De Borst, R., Brekelmans, W.A.M., De Vree, J.H.P.: Gradient enhanced damage for quasi-brittle materials. Int. J. Numer. Methods Eng. 39(19), 3391–3403 (1996)

    Article  MATH  Google Scholar 

  21. Borden, M.J., Verhoosel, C.V., Scott, M.A., Hughes, T.J., Landis, C.M.: A phase-field description of dynamic brittle fracture. Comput. Methods Appl. Mech. Eng. 217, 77–95 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  22. Miehe, C., Hofacker, M., Welschinger, F.: A phase field model for rate-independent crack propagation: robust algorithmic implementation based on operator splits. Comput. Methods Appl. Mech. Eng. 199(45), 2765–2778 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  23. Gerasimov, T., De Lorenzis, L.: A line search assisted monolithic approach for phase-field computing of brittle fracture. Comput. Methods Appl. Mech. Eng. 312, 276–303 (2016)

    Article  MathSciNet  Google Scholar 

  24. Broumand, P., Khoei, A.: X-FEM modeling of dynamic ductile fracture problems with a nonlocal damage-viscoplasticity model. Finite Elem. Anal. Des. 99, 49–67 (2015)

    Article  Google Scholar 

  25. Mazars, J.: PijaudierCabot, G.: Continuum damage theory application to concrete. J. Eng. Mech. 115(2), 345–365 (1989)

    Google Scholar 

  26. Osher, S., Sethian, J.A.: Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations. J. Comput. Phys. 79(1), 12–49 (1988)

    Article  MathSciNet  MATH  Google Scholar 

  27. Fries, T.P., Baydoun, M.: Crack propagation with the extended finite element method and a hybrid explicit-implicit crack description. Int. J. Numer. Methods Eng. 89(12), 1527–1558 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  28. Gravouil, A., Moës, N., Belytschko, T.: Non-planar 3D crack growth by the extended finite element and level sets-part II: level set update. Int. J. Numer. Methods Eng. 53(11), 2569–2586 (2002)

    Article  MATH  Google Scholar 

  29. Loehnert, S., Mueller-Hoeppe, D.S., Wriggers, P.: 3D corrected XFEM approach and extension to finite deformation theory. Int. J. Numer. Methods Eng. 86(4–5), 431–452 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  30. Sukumar, N., Chopp, D., Moran, B.: Extended finite element method and fast marching method for three-dimensional fatigue crack propagation. Eng. Fract. Mech. 70(1), 29–48 (2003)

    Article  Google Scholar 

  31. Oliver, J., Huespe, A.: Continuum approach to material failure in strong discontinuity settings. Comput. Methods Appl. Mech. Eng. 193(30), 3195–3220 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  32. Sukumar, N., Mos, N., Moran, B., Belytschko, T.: Extended finite element method for three-dimensional crack modelling. Int. J. Numer. Methods Eng. 48(11), 1549–1570 (2000)

    Google Scholar 

  33. Newmark, N.M., Asce, F.: A method of computation for structural dynamics. J. Eng. Mech. Div. 85, 67–94 (1959)

    Google Scholar 

  34. Menouillard, T., Réthoré, J., Combescure, A., Bung, H.: Efficient explicit time stepping for the eXtended Finite Element Method (X-FEM). Inter. J. Numer. Methods Eng. 68(9), 911–939 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  35. Menouillard, T., Réthoré, J., Moës, N., Combescure, A., Bung, H.: Mass lumping strategies for X-FEM explicit dynamics: application to crack propagation. Int. J. Numer. Methods Eng. 74(3), 447–474 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  36. Shahbeyk, S., Yaghoobi, M., Vafai, A.: Explicit dynamics X-FEM simulation of heterogeneous materials. Finite Elem. Anal. Des. 56, 52–79 (2012)

    Article  Google Scholar 

  37. Holl, M.: Multiscale crack-propagation and crack coalescence using the XFEM. Ph.D. thesis, Leibniz Universität Hannover (2014)

    Google Scholar 

  38. Holl, M., Rogge, T., Loehnert, S., Wriggers, P., Rolfes, R.: 3D multiscale crack propagation using the XFEM applied to a gas turbine blade. Comput. Mech. 53(1), 173–188 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  39. Lemaitre, J.: A Course on Damage Mechanics. Springer, Berlin (1996)

    Google Scholar 

  40. Comi, C., Mariani, S., Perego, U.: An extended FE strategy for transition from continuum damage to mode I cohesive crack propagation. Int. J. Numer. Anal. Methods Geomech. (2007)

    Google Scholar 

  41. Seabra, M.R.R., Šuštarič, P., Cesar de Sa, J.M.A., Rodič, T.: Damage driven crack initiation and propagation in ductile metals using XFEM. Comput. Mech. 52(1), 161–179 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  42. Pijaudier-Cabot, G., Benallal, A.: Strain localization and bifurcation in a nonlocal continuum. Int. J. Solids Struct. 30(13), 1761–1775 (1993)

    Article  MATH  Google Scholar 

  43. Areias, P.M.A., Belytschko, T.: Analysis of three-dimensional crack initiation and propagation using the extended finite element method. Int. J. Numer. Meth. Eng. 63(5), 760–788 (2005)

    Article  MATH  Google Scholar 

  44. Combescure, A., Gravouil, A., Grégoire, D., Réthoré, J.: X-FEM a good candidate for energy conservation in simulation of brittle dynamic crack propagation. Comput. Methods Appl. Mech. Eng. 197(5), 309–318 (2008)

    Article  MATH  Google Scholar 

  45. Grégoire, D., Maigre, H., Réthoré, J., Combescure, A.: Dynamic crack propagation under mixed-mode loading comparison between experiments and X-FEM simulations. Int. J. Solids Struct. 44(20), 6517–6534 (2007)

    Google Scholar 

  46. Wells, G.N., Sluys, L.J., de Borst, R.: Simulating the propagation of displacement discontinuities in a regularized strain-softening medium. Int. J. Numer. Methods Eng. 53(5), 1235–1256 (2002)

    Article  Google Scholar 

  47. Kalthoff, J.F.: Shadow optical analysis of dynamic shear fracture. Opt. Eng. 27(10), 271035–271035 (1988)

    Google Scholar 

  48. Kalthoff, J.F.: Modes of dynamic shear failure in solids. Int. J. Fract. 101(1/2), 1–31 (2000)

    Article  Google Scholar 

  49. Elguedj, T., Gravouil, A., Maigre, H.: An explicit dynamics extended finite element method. Part 1: mass lumping for arbitrary enrichment functions. Comput. Methods Appl. Mech. Eng. 198(30), 2297–2317 (2009)

    Article  MATH  Google Scholar 

  50. Moreau, K., Moës, N., Picart, D., Stainier, L.: Explicit dynamics with a non-local damage model using the thick level set approach. Int. J. Numer. Methods Eng. 102(3–4), 808–838 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  51. Borden, M.J.: Isogeometric analysis of phase-field models for dynamic brittle and ductile fracture. Ph.D. thesis (2012)

    Google Scholar 

  52. Zhou, M., Rosakis, A., Ravichandran, G.: On the growth of shear bands and failure-mode transition in prenotched plates: a comparison of singly and doubly notched specimens. Int. J. Plast. 14(4), 435–451 (1998)

    Article  MATH  Google Scholar 

  53. Ravi-Chandar, K., Lu, J., Yang, B., Zhu, Z.: Failure mode transitions in polymers under high strain rate loading. Int. J. Fract. 101(1/2), 33–72 (2000)

    Article  Google Scholar 

  54. Batra, R., Ravinsankar, M.: Three-dimensional numerical simulation of the Kalthoff experiment. Int. J. Fract. 105(2), 161–186 (2000)

    Article  Google Scholar 

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Acknowledgements

The German Research Association (DFG) is gratefully acknowledged for the support of the IRTG 1627 program.

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Authors and Affiliations

  1. Institute of Continuum Mechanics, Leibniz Universität Hannover, Appelstr. 11A, 30167, Hanover, Germany

    M. Pezeshki, S. Loehnert & P. Wriggers

  2. LMT/ENS Cachan/CNRS/Université Paris-Saclay, 94235, Cachan, France

    P. A. Guidault & E. Baranger

Authors
  1. M. Pezeshki
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  2. S. Loehnert
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  3. P. Wriggers
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  4. P. A. Guidault
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  5. E. Baranger
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Corresponding author

Correspondence to M. Pezeshki .

Editor information

Editors and Affiliations

  1. University of Zagreb, Zagreb, Croatia

    Jurica Sorić

  2. Institute of Continuum Mechanics, Leibniz Universität Hannover, Hannover, Germany

    Peter Wriggers

  3. LMT Cachan, Cachan, France

    Olivier Allix

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Pezeshki, M., Loehnert, S., Wriggers, P., Guidault, P.A., Baranger, E. (2018). 3D Dynamic Crack Propagation by the Extended Finite Element Method and a Gradient-Enhanced Damage Model. In: Sorić, J., Wriggers, P., Allix, O. (eds) Multiscale Modeling of Heterogeneous Structures. Lecture Notes in Applied and Computational Mechanics, vol 86. Springer, Cham. https://doi.org/10.1007/978-3-319-65463-8_14

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  • DOI: https://doi.org/10.1007/978-3-319-65463-8_14

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