107
Views
3
CrossRef citations to date
0
Altmetric
Original Articles

Scaled boundary finite element method for calculating the J-integral based on LEFM

ORCID Icon &
Pages 3817-3828 | Received 06 Dec 2022, Accepted 24 Feb 2023, Published online: 06 Mar 2023

References

  • T. L. Anderson, Fracture Mechanics: Fundamentals and Applications, 3rd ed., CRC press, New York, 2005.
  • M. Fan, Z. M. Xiao, and J. Luo, Application of cohesive zone model in crack propagation analysis in multiphase composite materials, Mech. Adv. Mater. Struct., vol. 24, no. 13, pp. 1109–1115, 2017. DOI: 10.1080/15376494.2016.1227495.
  • R. Panian and M. Yazdani, Estimation of the service load capacity of plain concrete arch bridges using a novel approach: Stress intensity factor, Structures, vol. 27, pp. 1521–1534, 2020. DOI: 10.1016/j.istruc.2020.07.055.
  • Y.-J. Wang, Z.-M. Wu, F.-M. Qu, W. Zhang, Numerical investigation on crack propagation process of concrete gravity dams under static and dynamic loads with in-crack reservoir pressure, Theor. Appl. Fract. Mech., vol. 117, pp. 103221, 2022. DOI: 10.1016/j.tafmec.2021.103221.
  • E. Alizadeh and M. Dehestani, Theoretical and numerical fracture analysis of bovine cortical bone under tensile loading in mode I and mixed-mode fracture, Mech. Adv. Mater. Struct., vol. 29, no. 26, pp. 5311–5325, 2022. DOI: 10.1080/15376494.2021.1953645.
  • J. R. Rice, A path independent integral and the approximate analysis of strain concentration by notches and cracks, J. Appl. Mech., vol. 35, no. 2, pp. 379–386, 1968. DOI: 10.1115/1.3601206.
  • G. P. Cherepanov, Crack propagation in continuous media, J. Appl. Math. Mech., vol. 31, no. 3, pp. 503–512, 1967. DOI: 10.1016/0021-8928(67)90034-2.
  • M. Yazdani and N. Khaji, Development of decoupled equations method to calculate J-integral in 2D problems, Modares Mech. Eng., vol. 15, no. 9, pp. 59–68, 2015.
  • Y. Q. He, H. T. Yang, and A. J. Deeks, Determination of coefficients of crack tip asymptotic fields by an element-free Galerkin scaled boundary method, Fatigue Fract. Eng. Mater. Struct., vol. 35, no. 8, pp. 767–785, 2012. DOI: 10.1111/j.1460-2695.2012.01662.x.
  • G. Derbalian, J-integral estimation procedures, J. Pressure Vessel Technol., vol. 105, no. 4, pp. 299–308, 1983. DOI: 10.1115/1.3264284.
  • V. A. Bazhenov, A. I. Gulyar, S. O. Piskunov, A.S. Sakharov, A.A. Shryl' and Y.V. Maksimyuk, Solving linear and nonlinear three-dimensional problems of fracture mechanics by a semi-analytic finite element method. Part 2. A procedure for computing the invariant J-integral in fem discrete models, Strength Mater., vol. 43, no. 2, pp. 122–133, 2011. DOI: 10.1007/s11223-011-9278-9.
  • H. Yu, T. Sumigawa, and T. Kitamura, A domain-independent interaction integral for linear elastic fracture analysis of micropolar materials, Mech. Mater., vol. 74, pp. 1–13, 2014. DOI: 10.1016/j.mechmat.2014.03.001.
  • E. Roos, U. Eisele, and H. Silcher, A procedure for the experimental assessment of the J-integral by means of specimens of different geometries, Int. J. Press. Vessels Pip., vol. 23, no. 2, pp. 81–93, 1986. DOI: 10.1016/0308-0161(86)90012-8.
  • D. Nunez, K. S. Surana, A. Romkes, and J. N. Reddy, J-Integral for mode i linear elastic fracture mechanics in h, p, k mathematical and computational framework, Int. J. Comput. Methods Eng. Sci. Mech., vol. 10, no. 5, pp. 345–369, 2009. DOI: 10.1080/15502280903106481.
  • E. T. Ooi, Z. J. Yang, and Z. Y. Guo, Dynamic cohesive crack propagation modelling using the scaled boundary finite element method, Fatigue Fract. Eng. Mater. Struct., vol. 35, no. 8, pp. 786–800, 2012. DOI: 10.1111/j.1460-2695.2011.01652.x.
  • P. Zakian and N. Khaji, A stochastic spectral finite element method for solution of faulting-induced wave propagation in materially random continua without explicitly modeled discontinuities, Comput. Mech., vol. 64, no. 4, pp. 1017–1048, 2019. DOI: 10.1007/s00466-019-01692-5.
  • C. Song, E. T. Ooi, and S. Natarajan, A review of the scaled boundary finite element method for two-dimensional linear elastic fracture mechanics, Eng. Fract. Mech., vol. 187, pp. 45–73, 2018. DOI: 10.1016/j.engfracmech.2017.10.016.
  • S. D. Daxini and J. M. Prajapati, A review on recent contribution of meshfree methods to structure and fracture mechanics applications, Sci. World J., vol. 2014, pp. 1–13, 2014. DOI: 10.1155/2014/247172.
  • A. Sedmak, Computational fracture mechanics: An overview from early efforts to recent achievements, Fatigue Fract. Eng. Mater. Struct., vol. 41, no. 12, pp. 2438–2474, 2018. DOI: 10.1111/ffe.12912.
  • R. D. Henshell and K. G. Shaw, Crack tip finite elements are unnecessary, Int. J. Numer. Meth. Eng., vol. 9, no. 3, pp. 495–507, 1975. DOI: 10.1002/nme.1620090302.
  • T. Belytschko and T. Black, Elastic crack growth in finite elements with minimal remeshing, Int. J. Numer. Meth. Eng., vol. 45, no. 5, pp. 601–620, 1999. DOI: 10.1002/(SICI)1097-0207(19990620)45:5<601::AID-NME598>3.0.CO;2-S.
  • T. Belytschko, Y. Y. Lu, and L. Gu, Element-free Galerkin methods, Int. J. Numer. Meth. Eng., vol. 37, no. 2, pp. 229–256, 1994. DOI: 10.1002/nme.1620370205.
  • T. A. Cruse and W. Vanburen, Three-dimensional elastic stress analysis of a fracture specimen with an edge crack, Int. J. Fract., vol. 7, no. 1, pp. 1–15, 1971. DOI: 10.1007/BF00236479.
  • A. Portela, M. H. Aliabadi, and D. P. Rooke, Dual boundary element incremental analysis of crack propagation, Comput. Struct., vol. 46, no. 2, pp. 237–247, 1993. DOI: 10.1016/0045-7949(93)90189-K.
  • R. Simpson and J. Trevelyan, A partition of unity enriched dual boundary element method for accurate computations in fracture mechanics, Comput. Methods Appl. Mech. Eng., vol. 200, no. 1–4, pp. 1–10, 2011. DOI: 10.1016/j.cma.2010.06.015.
  • M. Mousavi, S. Hamzehei-Javaran, and S. Shojaee, A new insight into analysis of linear elastic fracture mechanics with spherical Hankel boundary elements, Theor. Appl. Fract. Mech., vol. 115, pp. 103059, 2021. DOI: 10.1016/j.tafmec.2021.103059.
  • M. Yazdani, A novel modification of decouple scaled boundary finite element method in fracture mechanics problems, J. Comput. Appl. Res. Mech. Eng. (JCARME), vol. 7, no. 2, pp. 243–260, 2018.
  • N. Khaji, and M. Yazdani, Determination of stress intensity factors of 2D fracture mechanics problems through a new semi-analytical method, Fatigue Fract. Eng. Mater. Struct., vol. 39, no. 4, pp. 467–478, 2016. DOI: 10.1111/ffe.12375.
  • S. R. Chidgzey and A. J. Deeks, Determination of coefficients of crack tip asymptotic fields using the scaled boundary finite element method, Eng. Fract. Mech., vol. 72, no. 13, pp. 2019–2036, 2005. DOI: 10.1016/j.engfracmech.2004.07.010.
  • Z. Yang, Fully automatic modelling of mixed-mode crack propagation using scaled boundary finite element method, Eng. Fract. Mech., vol. 73, no. 12, pp. 1711–1731, 2006. DOI: 10.1016/j.engfracmech.2006.02.004.
  • M. Yazdani, N. Khaji, and M. I. Khodakarami, Development of a new semi-analytical method in fracture mechanics problems based on the energy release rate, Acta Mech., vol. 227, no. 12, pp. 3529–3547, 2016. DOI: 10.1007/s00707-016-1685-3.
  • M. Yazdani and N. Khaji, Development of a new semianalytical approach for 2D analysis of crack propagation problems, Fatigue Fract. Eng. Mater. Struct., vol. 41, no. 6, pp. 1344–1363, 2018. DOI: 10.1111/ffe.12778.
  • S. Hell and W. Becker, An enriched scaled boundary finite element method for 3D cracks, Eng. Fract. Mech., vol. 215, pp. 272–293, 2019. DOI: 10.1016/j.engfracmech.2019.04.032.
  • E. T. Ooi, M. D. Iqbal, C. Birk, S. Natarajan, E.H. Ooi, C. Song, A polygon scaled boundary finite element formulation for transient coupled thermoelastic fracture problems, Eng. Fract. Mech., vol. 240, pp. 107300, 2020. DOI: 10.1016/j.engfracmech.2020.107300.
  • M. D. Iqbal, C. Birk, E. T. Ooi, and H. Gravenkamp, Development of the scaled boundary finite element method for crack propagation modeling of elastic solids subjected to coupled thermo-mechanical loads, Comput. Methods Appl. Mech. Eng., vol. 387, pp. 114106, 2021. DOI: 10.1016/j.cma.2021.114106.
  • S. Jiang, L. Sun, E. T. Ooi, M. Ghaemian, and C. Du, Automatic mesoscopic fracture modelling of concrete based on enriched SBFEM space and quad-tree mesh, Constr. Build. Mater., vol. 350, pp. 128890, 2022. DOI: 10.1016/j.conbuildmat.2022.128890.
  • G. E. Bird, J. Trevelyan, and C. E. Augarde, A coupled BEM/scaled boundary FEM formulation for accurate computations in linear elastic fracture mechanics, Eng. Anal. Bound. Elem., vol. 34, no. 6, pp. 599–610, 2010. DOI: 10.1016/j.enganabound.2010.01.007.
  • E. T. Ooi and Z. J. Yang, A hybrid finite element-scaled boundary finite element method for crack propagation modelling, Comput. Methods Appl. Mech. Eng., vol. 199, no. 17-20, pp. 1178–1192, 2010. DOI: 10.1016/j.cma.2009.12.005.
  • B. Chen, T. Yu, S. Natarajan, Q. Zhang, and T.Q. Bui, Three-dimensional dynamic and quasi-static crack growth by a hybrid XFEM-peridynamics approach, Eng. Fract. Mech., vol. 261, pp. 108205, 2022. DOI: 10.1016/j.engfracmech.2021.108205.
  • A. Portela, M. H. Aliabadi, and D. P. Rooke, The dual boundary element method: Effective implementation for crack problems, Int. J. Numer. Meth. Engng., vol. 33, no. 6, pp. 1269–1287, 1992. DOI: 10.1002/nme.1620330611.
  • T. Nishioka and S. N. Atluri, Path-independent integrals, energy release rates, and general solutions of near-tip fields in mixed-mode dynamic fracture mechanics, Eng. Fract. Mech., vol. 18, no. 1, pp. 1–22, 1983. DOI: 10.1016/0013-7944(83)90091-7.
  • S. Jiang, C. Wan, L. Sun, and D. Du, Flaw classification and detection in thin-plate structures based on scaled boundary finite element method and deep learning, Numer. Meth. Eng., vol. 123, no. 19, pp. 4674–4701, 2022. DOI: 10.1002/nme.7051.
  • L. Lehmann, S. Langer, and D. Clasen, Scaled boundary finite element method for acoustics, J. Comp. Acous., vol. 14, no. 04, pp. 489–506, 2006. DOI: 10.1142/S0218396X06003141.
  • E. T. Ooi, A. Saputra, S. Natarajan, E. H. Ooi, and C. Song, A dual scaled boundary finite element formulation over arbitrary faceted star convex polyhedra, Comput. Mech., vol. 66, no. 1, pp. 27–47, 2020. DOI: 10.1007/s00466-020-01839-9.
  • G. Lin, P. Zhang, J. Liu, and J. Li, Analysis of laminated composite and sandwich plates based on the scaled boundary finite element method, Compos. Struct., vol. 187, pp. 579–592, 2018. DOI: 10.1016/j.compstruct.2017.11.001.
  • S.-y. Jiang, C.-b. Du, and E. T. Ooi, Modelling strong and weak discontinuities with the scaled boundary finite element method through enrichment, Eng. Fract. Mech., vol. 222, pp. 106734, 2019. DOI: 10.1016/j.engfracmech.2019.106734.
  • S. Natarajan, J. Wang, C. Song, and C. Birk, Isogeometric analysis enhanced by the scaled boundary finite element method, Comput. Methods Appl. Mech. Eng., vol. 283, pp. 733–762, 2015. DOI: 10.1016/j.cma.2014.09.003.
  • J. P. Wolf and C. Song, Scaled boundary finite-element method—a primer: Derivations, Comput. Struct., vol. 78, no. 1–3, pp. 191–210, 2000. DOI: 10.1016/S0045-7949(00)00099-7.
  • C. Song and J. P. Wolf, Scaled boundary finite-element method—a primer: Solution procedures, Comput. Struct., vol. 78, nos. 1–3, pp. 211–225, 2000. DOI: 10.1016/S0045-7949(00)00100-0.
  • S. Dai, C. Augarde, C. Du, and D. Chen, A fully automatic polygon scaled boundary finite element method for modelling crack propagation, Eng. Fract. Mech., vol. 133, pp. 163–178, 2015. DOI: 10.1016/j.engfracmech.2014.11.011.
  • S. Mohammadi, Extended finite element method: For fracture analysis of structures, 2008.
  • H. Tada, P. C. Paris, and G. R. Irwin, The stress analysis of cracks, Handbook, Del Research Corporation, vol. 34, pp. 635, 1973.
  • ANSYS. Commercial Finite Element Package, 19.0. USA: 2019.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.