Abstract
Fracture propagation simulations by means of the traditional Finite Element Method require progressive remeshing to match the geometry of the discontinuity, which heavily increases the computational effort. To overcome this limitation, methods like the eXtended Finite Element Method (XFEM), in which element nodes are enriched through the medium of Heaviside step function multiplied by nodal shape functions, may be used. The addition of a discontinuous field allows the full crack geometry to be modelled independently of the mesh, eliminating the need to remesh altogether. In this paper OpenSees framework has been used to evaluate crack propagation in brittle materials by means of the XFEM method. Two shell-type XFEM elements have been implemented into OpenSees: a three-node triangular element and a four-node quadrangular element. These elements are an improvement of the elements with drilling degrees of freedom lately suggested by the Authors [6]. The implementation of XFEM elements implied some major modifications directly into OpenSees code to take into account the rise of number of degrees of freedom in the enriched element nodes during the analysis. The developed XFEM elements have been used to evaluate crack propagation into a plane shell subject to monotonically increasing loads. Moreover, with due tuning, the modified XFEM OpenSees code can be used to study also other problems such as material discontinuities, complex geometries and contact problems.
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References
Belytschko, T., Black, T.: Elastic crack growth in finite element with minimal remeshing. Int. J. Numer. Meth. Eng. 45(5), 601–620 (1999)
Moës, N., Dolbow, J., Belytschko, T.: A finite element method for crack growth without remeshing. Int. J. Numer. Meth. Eng. 46(1), 131–150 (1999)
Ventura, G.: On the elimination of quadrature subcells for discontinuous functions in the eXtended finite-element method. Int. J. Numer. Meth. Eng. 66, 761–795 (2006)
Ventura, G., Benvenuti, E.: Equivalent polynomials for quadrature in Heaviside function enriched elements. Int. J. Numer. Meth. Eng. 102, 688–710 (2015)
Mariggiò, G., Fichera, S., Corrado, M., Ventura, G.: EQP - A 2D/3D library for integration of polynomials times step function. SoftwareX 12, 100636 (2020). https://doi.org/10.1016/j.softx.2020.100636
Fichera, S., Biondi, B.: Implementation into OpenSees of triangular and quadrangular shell finite elements with drilling degrees of freedom. In: Proceedings of OpenSees Days Eurasia 2019, The Hong Kong Polytechnic University (2019)
Bathe, K.-J.: Finite Element Procedures, 2nd edn., Watertown, MA (2014)
Belytschko, T., Liu, W.K., Moran, B., Elkhodary, K.: Nonlinear Finite Elements for Continua and Structures, 2nd edn. Wiley (2014)
Belytschko, T., Gracie, R., Ventura, G.: A review of extended/generalized finite element methods for material modeling. Model Simul. Mater. Sci. Eng. 17, 1–24 (2009)
Lv, J.-H., Jiao, Y.-Y., Rabczuk, T., Zhuang, X.-Y., Feng, X.-T., Tan, F.: A general algorithm for numerical integration of three-dimensional crack singularities in PU-based numerical methods. Comput. Methods Appl. Mech. Eng. 363, 112908–1 (2020)
Düster, A., Allix, O.: Selective enrichment of moment fitting and application to cut finite elements and cells. Comput. Mech. 65(2), 429–450 (2019). https://doi.org/10.1007/s00466-019-01776-2
Surendran, M., Natarajan, S., Palani, G., Bordas, S.: Linear smoothed extended finite element method for fatigue crack growth simulations. Eng. Fract. Mech. 206, 551–564 (2019)
Müller, B., Krämer-Eis, S., Kummer, F., Oberlack, M.: A high-order discontinuous Galerkin method for compressible flows with immersed boundaries. Int. J. Numer. Methods Eng. 110(1), 3–30 (2017)
Saye, R.: High-order quadrature methods for implicitly defined surfaces and volumes in hyperrectangles. SIAM J. Sci. Comput. 37(2), A993–A1019 (2015)
Martin, A., Esnault, J.-B., Massin, P.: About the use of standard integration schemes for X-FEM in solid mechanics plasticity. Comput. Methods Appl. Mech. Eng. 283, 551–572 (2015)
Sudhakar, Y., Moitinho de Almeida, J., Wall, W.: An accurate, robust, and easyto-implement method for integration over arbitrary polyhedra: application to embedded interface methods. J. Comput. Phys. 273, 393–415 (2014)
Alves, P., Barros, F., Pitangueira, R.: An object-oriented approach to the generalized finite element method. Adv. Eng. Softw. 59, 1–18 (2013)
Mousavi, S., Sukumar, N.: Numerical integration of polynomials and discontinuous functions on irregular convex polygons and polyhedrons. Comput. Mech. 47(5), 535–554 (2011)
Chin, E., Lasserre, J., Sukumar, N.: Modeling crack discontinuities without element-partitioning in the extended finite element method. Int. J. Numer, Methods Eng. 110(11), 1021–1048 (2017)
Scholz, F., Mantzaflaris, A., Jüttler, B.: First order error correction for trimmed quadrature in isogeometric analysis. In: Apel, T., Langer, U., Meyer, A., Steinbach, O. (eds.) FEM 2017. LNCSE, vol. 128, pp. 297–321. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-14244-5_15
Stroud, A.: Approximate Calculation of Multiple Integrals. Prentice Hall, Englewood Cliffs (1971)
Zienkiewicz, O.C., Taylor, R.L., Zhu, J.Z.: The Finite Element Method: Its Basis and Fundamentals, 6th edn. Butterworth-Heinemann (2005)
Amazigo, J., Rubenfeld, L.: Advanced Calculus and its Application to the Engineering and Physical Science. Wiley, Hoboken (1980)
Davis, P.J., Rabinowitz, P.: Methods of numerical Integration, 2nd edn. Academic Press (1984)
Song, C., Zhang, H., Wu, Y., Bao, H.: Cutting and fracturing models without remeshing. In: Chen, F., Jüttler, B. (eds.) GMP 2008. LNCS, vol. 4975, pp. 107–118. Springer, Heidelberg (2008). https://doi.org/10.1007/978-3-540-79246-8_8
Iben, H.N., O’Brien, J.F.: Generating surface crack patterns. Graph Models 71(6), 198–208 (2009). https://doi.org/10.1016/j.gmod.2008.12.005
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Fichera, S., Biondi, B., Ventura, G. (2023). Implementation into OpenSees of XFEM for Analysis of Crack Propagation in Brittle Materials. In: Di Trapani, F., Demartino, C., Marano, G.C., Monti, G. (eds) Proceedings of the 2022 Eurasian OpenSees Days. EOS 2022. Lecture Notes in Civil Engineering, vol 326. Springer, Cham. https://doi.org/10.1007/978-3-031-30125-4_14
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