Advertisement

Meshfree cohesive cracking method for dynamic material failure

Article

Abstract

We develop a cohesive meshfree crack method for material failure under dynamic loading conditions. Failure is modeled by discrete crack approach. Crack is represented by a set of cohesive crack segments that are restricted to lie on the nodes but which can be arbitrarily oriented. Propagation of the crack is achieved by activation of crack surfaces at individual nodes, so no representation of the crack surface is needed. The crack is modeled by local enrichment of the test and trial functions with sign function, so that discontinuities are along the direction of the crack. A set of cracking rules is developed to avoid spurious cracking. The method is applied to two problems and compared to experimental data and results of other researchers. The results are very promising.

Keywords

Material failure Meshfree method Fracture mechanics 

References

  1. Belytschko, T., Black, T.: Elastic crack growth in finite elements with minimal remeshing. Int. J. Numer. Methods Eng. 45, 601–620 (1999)MATHCrossRefMathSciNetGoogle Scholar
  2. Belytschko, T., Lu, Y.Y., Gu, L.: Crack propagation by element-free galkerin methods. Eng. Fract. Mech. 51, 295–315 (1994a)CrossRefGoogle Scholar
  3. Belytschko, T., Lu, Y.Y., Gu, L.: Element-free galerkin methods. Int. J. Numer. Methods Eng. 37, 229–256 (1994b)MATHCrossRefMathSciNetGoogle Scholar
  4. Belytschko, T., Krongauz, Y., Organ, D., Fleming, M., Krysl, P.: Meshless methods: An overview and recent developments. Comput. Methods Appl. Mech. Eng. 139, 3–47 (1996)MATHCrossRefGoogle Scholar
  5. Belytschko, T., Guo, Y., Liu, W.K., Xiao, S.P.: A unified stability analysis of meshfree particle methods. Int. J. Numer. Methods Eng. 48, 1359–1400 (2000)MATHCrossRefMathSciNetGoogle Scholar
  6. Bordas, S., Rabczuk, T., Zi, G.: Three-dimensional crack initiation, propagation, branching and junction in non-linear materials by extrinsic discontinuous enrichment of meshfree methods without asymptotic enrichment. Eng. Fract. Mech. 75, 943–960 (2008)CrossRefGoogle Scholar
  7. Fineberg, J., Sharon, E., Cohen, G.: Crack front waves in dynamic fracture. Int. J. Fract. 121, 55–69 (2003)CrossRefGoogle Scholar
  8. Fleming, M., Chu, Y.A., Moran, B., Belytschko, T.: Enriched element-free galerkin methods for crack tip fields. Int. J. Numer. Methods Eng. 40, 1483–1504 (1997)CrossRefMathSciNetGoogle Scholar
  9. Hao, S., Liu, W.K., Klein, P.A., Rosakis, A.J.: Modeling and simulation of intersonic crack growth. Int. J. Solids Struct. 41(7), 1773–1799 (2004)MATHCrossRefGoogle Scholar
  10. Kalthoff, J.F.: Modes of dynamic shear failure in solids. Int. J. Fract. 101, 1–31 (2000)CrossRefGoogle Scholar
  11. Kalthoff, J.F., Winkler, S.: Failure mode transition at high rates of shear loading. International Conference on Impact Loading and Dynamic Behavior of Materials, vol. 1, pp. 185–195 (1987)Google Scholar
  12. Li, S., Simonson, B.C.: Meshfree simulation of ductile crack propagation. Int. J. Comput. Methods Eng. Sci. Mech. 6, 1–19 (2003)MATHCrossRefGoogle Scholar
  13. Li, S., Simkins, D.C.: Conserving galerkin weak formulations for computational fracture mechanics. Commun. Numer. Methods Eng. 18, 835–850 (2002)MATHCrossRefMathSciNetGoogle Scholar
  14. Li, S., Hao, W., Liu, W.K.: Mesh-free simulations of shear banding in large deformation. Int. J. Solids Struct. 37, 7185–7206 (2000)MATHCrossRefGoogle Scholar
  15. Li, S., Liu, W.K., Rosakis, A., Belytschko, T., Hao, W.: Mesh free galerkin simulations of dynamic shear band propagation and failure mode transition. Int. J. Solids Struct. 39, 1213–1240 (2002)MATHCrossRefGoogle Scholar
  16. Nguyen, V.P., Rabczuk, T., Bordas, S., Duflot, M.: Meshless methods: a review and computer implementation aspects. Math. Comput. Simul. 79, 763–813 (2008)MATHCrossRefMathSciNetGoogle Scholar
  17. Pandolfi, A., Krysl, P., Ortiz, M.: Finite element simulation of ring expansion and fragmentation: The capturing of length and time scales through cohesive models of fracture. Int. J. Fract. 95, 279–297 (1999)Google Scholar
  18. Rabczuk, T., Areias, P.M.A.: A new approach for modelling slip lines in geological materials with cohesive models. Int. J. Numer. Anal. Methods Geomech. 30(11), 1159–1172 (2006a)CrossRefGoogle Scholar
  19. Rabczuk, T., Areias, P.: A meshfree thin shell for arbitrary evolving cracks based on an extrinsic basis. Comput. Model. Eng. Sci. 16(2), 115–130 (2006b)Google Scholar
  20. Rabczuk, T., Belytschko, T.: Cracking particles: a simplified meshfree method for arbitrary evolving cracks. Int. J. Numer. Methods Eng. 61(13), 2316–2343 (2004)MATHCrossRefGoogle Scholar
  21. Rabczuk, T., Belytschko, T.: Adaptivity for structured meshfree particle methods in 2d and 3d. Int. J. Numer. Methods Eng. 63(11), 1559–1582 (2005)MATHCrossRefMathSciNetGoogle Scholar
  22. Rabczuk, T., Belytschko, T.: Application of particle methods to static fracture of reinforced concrete structures. Int. J. Fract. 137(1-4), 19–49 (2006)CrossRefGoogle Scholar
  23. Rabczuk, T., Belytschko, T.: A three dimensional large deformation meshfree method for arbitrary evolving cracks. Comput. Methods Appl. Mech. Eng. 196, 2777–2799 (2007)MATHCrossRefMathSciNetGoogle Scholar
  24. Rabczuk, T., Samaniego, E.: Discontinuous modelling of shear bands using adaptive meshfree methods. Comput. Methods Appl. Mech. Eng. 197, 641–658 (2008)MATHMathSciNetGoogle Scholar
  25. Rabczuk, T., Zi, G.: A meshfree method based on the local partition of unity for cohesive cracks. Comput. Mech. 39(6), 743–760 (2007)MATHCrossRefGoogle Scholar
  26. Rabczuk, T., Belytschko, T., Xiao, S.P.: Stable particle methods based on lagrangian kernels. Comput. Methods Appl. Mech. Eng. 193, 1035–1063 (2004)MATHCrossRefMathSciNetGoogle Scholar
  27. Rabczuk, T., Bordas, S., Zi, G.: A three dimensional meshfree method for static and dynamic multiple crack nucleation/propagation with crack path continuity. Comput. Mech. 40(3), 473–495 (2007a)MATHCrossRefGoogle Scholar
  28. Rabczuk, T., Bordas, S., Zi, G.: A three-dimensional meshfree method for continuous multiple crack initiation, nucleation and propagation in statics and dynamics. Comput. Mech. 40(3), 473–495 (2007b)MATHCrossRefGoogle Scholar
  29. Rabczuk, T., Areias, P.M.A., Belytschko, T.: A simplified mesh-free method for shear bands with cohesive surfaces. Int. J. Numer. Methods Eng. 69(5), 993–1021 (2007c)CrossRefMathSciNetGoogle Scholar
  30. Rabczuk, T., Areias, P.M.A., Belytschko, T.: A meshfree thin shell method for non-linear dynamic fracture. Int. J. Numer. Methods Eng. 72(5), 524–548 (2007d)CrossRefMathSciNetGoogle Scholar
  31. Rabczuk, T., Zi, G., Bordas, S., Nguyen-Xuan, H.: A geometrically non-linear three dimensional cohesive crack method for reinforced concrete structures. Eng. Fract. Mech. 75, 4740–4758 (2008)CrossRefGoogle Scholar
  32. Rabczuk, T., Song, J.-H., Belytschko, T.: Simulations of instability in dynamic fracture by the cracking particles method. Eng. Fract. Mech. 76, 730–741 (2009)CrossRefGoogle Scholar
  33. Rabczuk, T., Gracie, R., Song, J.-H., Belytschko, T.: Immersed particle method for fluid-structure interaction. Int. J. Numer. Methods Eng. 81, 48–71 (2010)MATHMathSciNetGoogle Scholar
  34. Ravi-Chandar, K.: Dynamic fracture of nominally brittle materials. Int. J. Fract. 90, 83–102 (1998)CrossRefGoogle Scholar
  35. Sharon, E., Gross, P.S.P., Fineberg, J.: Local crack branching as a mechanism for instability in dynamic fracture. Phys. Rev. Lett. 74, 5096–5099 (1995)CrossRefGoogle Scholar
  36. Xu, X.P., Needleman, A.: Numerical simulations of fast crack growth in brittle solids. J. Mech. Phys. Solids 42, 1397–1434 (1994)MATHCrossRefGoogle Scholar
  37. Zhang, Y.Y.: Meshless modelling of crack growth with discrete rotating crack segments. Int. J. Mech. Mater. Design 4(1), 71–77 (2008)CrossRefGoogle Scholar
  38. Zi, G., Rabczuk, T., Wall, W.: Extended meshfree methods without branch enrichment for cohesive cracks. Comput. Mech. 40(2), 367–382 (2007)MATHCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, B.V. 2010

Authors and Affiliations

  1. 1.Department of Engineering MechanicsTsinghua UniversityBeijingChina

Personalised recommendations