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A technique for capturing structural crack geometry in numerical simulation based on the invariant level set method

  • Tao Wang (School of Civil Engineering, Central South University) ;
  • Shangtao Hu (School of Civil Engineering, Central South University) ;
  • Menggang Yang (School of Civil Engineering, Central South University) ;
  • Shujun Fang (School of Civil Engineering, Central South University)
  • Received : 2023.02.15
  • Accepted : 2023.06.29
  • Published : 2023.08.10

Abstract

Engineering structures usually suffer from cracks. The crack geometry has an influence on the structural mechanical properties and subsequent crack propagations. However, as an extensively utilized method in fracture analysis, the extended finite element method provided by Abaqus fails to output the specific location and dimensions of fractures. In this study, a technique to capture the crack geometry is proposed. The technique is based on the invariant level set method (I-LSM), which can avoid updating the level set function during crack development. The solution is achieved by an open-source plug-in programmed by Python. Three examples were performed to verify the effectiveness and robustness of the program. The result shows that the developed program can accurately output the crack geometry in both the 2D and 3D models. The open-source plug-in codes are included as supplementary material.

Keywords

Acknowledgement

The authors gratefully acknowledge the financial support for this research provided by the National Natural Science Foundation of China (grant numbers 52278232 and 51978667), the Science and Technology Research and Development Program Project of China State Railway Group Co., Ltd. (Major Special Project, No. 2021-Special-04-2).

References

  1. Agathos, K., Chatzi, E. and Bordas, S.P.A. (2016), "Stable 3D extended finite elements with higher order enrichment for accurate non planar fracture", Comput. Meth. Appl. Mech. Eng., 306, 19-46. http://doi.org/10.1016/j.cma.2016.03.023.
  2. Agathos, K., Ventura, G., Chatzi, E. and Bordas, S.P.A. (2018), "Stable 3D XFEM/vector level sets for non-planar 3D crack propagation and comparison of enrichment schemes", Int. J. Numer. Meth. Eng., 113(2), 252-276. http://doi.org/10.1002/nme.5611.
  3. Bechet, E., Minnebol, H., Moes, N. and Burgardt, B. (2005), "Improved implementation and robustness study of the X-FEM for stress analysis around cracks", Int. J. Numer. Meth. Eng., 64(8), 1033-1056. http://doi.org/10.1002/nme.1386.
  4. Belytschko, T. and Black, T. (1999), "Elastic crack growth in finite elements with minimal remeshing", Int. J. Numer. Meth. Eng., 45(5), 601-620. https://doi.org/10.1002/(SICI)1097-0207(19990620)45:5<601::AID-NME598>3.0.CO;2-S.
  5. Carpinteri, A. and Montagnoli, F. (2020), "Scaling and fractality in subcritical fatigue crack growth: Crack-size effects on Paris' law and fatigue threshold", Fatig. Fract. Eng. Mater. Struct., 43(4), 788-801. http://doi.org/10.1111/ffe.13184.
  6. Dolbow, J. and Belytschko, T. (1999), "A finite element method for crack growth without remeshing", Int. J. Numer. Meth. Eng., 46(1), 131-150. https://doi.org/10.1002/(SICI)1097-0207(19990910)46:1<131::AID-NME726>3.0.CO;2-J.
  7. Dolbow, J.E. (1999), "An extended finite element method with discontinuous enrichment for applied mechanics", Ph.D. Dissertation, Northwestern university, Evanston.
  8. Duan, N., Ma, X., Lu, S., Xu, W. and Wang, S. (2021), "Research on 3D improved extended finite element method for electric field of liquid nitrogen with bubbles", Appl. Sci-Basel., 11, 483911. http://doi.org/10.3390/app11114839.
  9. Fett, T., Munz, D., Geraghty, R.D. and White, K.W. (2000), "Influence of specimen geometry and relative crack size on the R-curve", Eng. Fract. Mech., 66(4), 375-386. http://doi.org/10.1016/S0013-7944(00)00026-6.
  10. Gupta, V. and Duarte, C.A. (2016), "On the enrichment zone size for optimal convergence rate of the Generalized/Extended Finite Element Method", Comput. Math. Appl., 72(3), 481-493. http://doi.org/10.1016/j.camwa.2016.04.043.
  11. Jiang, S. and Du, C. (2017), "Study on dynamic interaction between crack and inclusion or void by using XFEM", Struct. Eng. Mech., 63(3), 329-345. http://10.12989/sem.2017.63.3.329.
  12. Jiang, Y., Dong, J., Nie, D.F. and Zhang, X.Q. (2021), "XFEM with partial Heaviside function enrichment for fracture analysis", Eng. Fract. Mech., 241, 107375. https://doi.org/10.1016/j.engfracmech.2020.107375.
  13. John, P. and Shah, S.P. (1990), "Mixed mode fracture of concrete subjected to impact loading", J. Struct. Eng., ASCE, 116, 585-602. https://doi.org/10.1061/(ASCE)0733-9445(1990)116:3(585).
  14. Khalkar, V. and Logesh, K. (2022), "The effect of crack geometry on mode shapes of a cracked cantilever beam", Austr. J. Mech. Eng., 20(4), 969-980. http://doi.org/10.1080/14484846.2020.1766349.
  15. Khalkar, V. and Ramachandran, S. (2018), "The effect of crack geometry on stiffness of spring steel cantilever beam", J. Low Frequen. Noise Vib. Active Control, 37(4), 762-773. http://doi.org/10.1177/1461348418765959.
  16. Luo, Z., Zhang, N., Zhao, L., Zeng, J., Liu, P. and Li, N. (2020), "Interaction of a hydraulic fracture with a hole in poroelasticity medium based on extended finite element method", Eng. Anal. Bound. Elem., 115, 108-119. http://doi.org/10.1016/j.enganabound.2020.03.011.
  17. Osher, S. and Sethian, J.A. (1988), "Fronts propagating with curvature-dependent speed: Algorithms based on Hamilton-Jacobi formulations", J. Comput. Phys., 79(1), 12-49. https://doi.org/10.1016/0021-9991(88)90002-2.
  18. Ponnusami, S.A., Krishnasamy, J., Turteltaub, S. and Van der Zwaag, S. (2022), "Elucidating the effect of cohesive zone length in fracture simulations of particulate composites", Eng. Fract. Mech., 268, 108431. http://doi.org/10.1016/j.engfracmech.2022.108431.
  19. Rezanezhad, M., Lajevardi, S.A. and Karimpouli, S. (2019), "Effects of pore-crack relative location on crack propagation in porous media using XFEM method", Theor. Appl. Fract. Mech., 103, 102241. http://doi.org/10.1016/j.tafmec.2020.102529.
  20. Song, J., Areias, P.M.A. and Belytschko, T. (2006), "A method for dynamic crack and shear band propagation with phantom nodes", Int. J. Numer. Meth. Eng., 67(6), 868-893. http://doi.org/10.1002/nme.1652.
  21. Tada, H., Paris, P.C. and Irwin, G.R. (1985), The Stress Analysis of Cracks Handbook, 2nd Edition, Paris Productions Incorporated, St. Louis, Missouri, USA.
  22. Tang, Y. and Chen, H. (2019), "Characterizations on fracture process zone of plain concrete", J. Civil Eng. Manage., 25(8), 819-830. http://doi.org/10.3846/jcem.2019.10799.
  23. TerMaath, S.C., Phoenix, S.L. and Hui, C.Y. (2006), "A technique for studying interacting cracks of complex geometry in 2D", Eng. Fract. Mech., 73(8), 1086-1114. http://doi.org/10.1016/j.engfracmech.2004.09.009.
  24. Tinh, Q.B. and Zhang, C. (2013), "Analysis of generalized dynamic intensity factors of cracked magnetoelectroelastic solids by X-FEM", Finite. Elem. Anal. Des., 69, 19-36. http://doi.org/10.1016/j.finel.2013.02.001.
  25. Wang, K., Zhang, Q., Xia, X., Wang, L. and Liu, X. (2015), "Analysis of hydraulic fracturing in concrete dam considering fluid-structure interaction using XFEM-FVM model", Eng. Fail. Anal., 57, 399-412. http://doi.org/10.1016/j.engfailanal.2015.07.012.
  26. Wang, Q., Zhang, G., Tong, Y. and Gu, C. (2021), "A numerical study on chloride diffusion in cracked concrete", Crystal., 11, 7427. http://doi.org/10.3390/cryst11070742.
  27. Wu, J. and Li, F. (2015), "An improved stable XFEM (Is-XFEM) with a novel enrichment function for the computational modeling of cohesive cracks", Comput. Meth. Appl. Mech. Eng., 295, 77-107. http://doi.org/10.1016/j.cma.2015.06.018.
  28. Zhang, H.H., Rong, G. and Li, L.X. (2010), "Numerical study on deformations in a cracked viscoelastic body with the extended finite element method", Eng. Anal. Bound. Elem., 34(6), 619-624. http://doi.org/10.1016/j.enganabound.2010.02.001.
  29. Zhang, K., Lu, F., Peng, Y. and Li, X. (2022), "A novel method for generation and prediction of crack propagation in gravity dams", Struct. Eng. Mech., 81(6), 665-675. https://doi.org/10.12989/sem.2022.81.6.665.