PSI - Issue 23

Michal Jedlička et al. / Procedia Structural Integrity 23 (2019) 445– 450 Michal Jelička, Václav Rek, Ji ří Vala / Structural Integrity Procedia 00 (2019) 000 – 000

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4. Illustrative example

A simple model has been prepared for the testing of the implemented XFEM functionality. In our illustrative ex ample we have finite hexahedral elements everywhere. The deformable body Ω has the total size 5  5  1 m, whereas the initial mesh size is also 1 m. The body is supported completely on its lower surface; the applied tension on its upper surface is 10 000 kN/m 2 . The Young modulus was E = 28 300 N/mm 2 , the Poisson ratio μ = 0,2. Fig. 6 demonstrates the simulation result: the distribution of deformation (the absolute value of u ) is evident from its left-hand part a); its right-hand part sketches the finite element decomposition, including the Gaussian inte gration points. Extended finite element technique has been implemented into the existing NE-XX solver for the 3-dimensional models with hexahedral and tetrahedral elements. Apart from the strong model simplifications, preliminary results (more extensive than those documented by Fig. 6) seem to produce results in good agreement with experiments. Nevertheless, reliable simulation of the crack propagation cannot be performed utilizing such quasi-static approach. The complete project of the RFEM-based software development relies on the implementation of damage analysis functions in several steps; only the first one has been announced in this paper. The next work for the near future should implement proper intensity stress factors, working with the Irwin-like criterion, or some with some alterna tive nonlocal computational approach. Babuška, I., Melenk, J. M., 1997. The partition of unity method. International Journal for Numerical Methods in Engineering 4 0, 727 – 758. Belytschko, T., Black, T., 1999. Elastic crack growth in finite elements with minimal remeshing. International Journal for Numerical Methods in Engineering 45, 601 – 620. Fries, T.-P., Belytschko, T., 2006. The intrinsic XFEM: a method for arbitrary discontinuities without additional unknowns. International Journal for Numerical Methods in Engineering 68, 1358 – 1385. Huynh, H. D., Nguyen, M. N., Cusatis, G., Tanaka, S., Bui, T. Q., 2019. A polygonal XFEM with new numerical integration for l inear elastic fracture mechanics. Engineering Fracture Mechanics 213, 241 – 263. Jirásek, J. , 2002. Numerical modeling of strong discontinuities. Revue francaise de génie civil 6, 1133 – 1146. Jirásek, J. , Belytschko, T., 2002. Computational resolution of strong discontinuities. In: Fifth World Congress on Computational Mechanics (WCCM V) in Vienna (2002, Mang. H. A., Rammerstorfer, F. G., eds.), 1 – 20. Kaliske, M., Dal, H., Fleischhauer, R., Jenkel, C., Netzker, C., 2012. Characterization of fracture processes by continuum and discrete modelling. Computational Mechanics 50, 303 – 320. Khoei, A. R., 2015. Extended Finite Element Method: Theory and Applications. J. Wiley & Sons, Hoboken. Kol ář , V., N ě mec, I., 1986. NE-XX: A finite element program system. Structural Analysis Systems: Software, Hardware, Capability, Compatibil ity, Applications 1, 141 – 150. Melenk, J. M., Babuška, I. , 1996. The partition of unity finite element method: basic theory and applications. Computer Methods in Applied Mechanics and Engineering 139, 289 – 314. Ottosen, N. S., Ristinmaa, M., 2013. Thermodynamically based fictitious crack/interface model for general normal and shear loading. Interna tional Journal of Solids and Structures 50, 3555 – 3561. Pike, M. G., Oskay, C., 2005. XFEM modeling of short microfiber reinforced composites with cohesive interfaces. Finite Elements in Analysis and Design 106, 16 – 31. Sih, G. C., 2009. Crack tip mechanics based on progressive damage of arrow:Hierarchy of singularities and multiscale segments. Theoretical and Applied Fracture Mechanics 51, 11 – 32. Song, J.-H., Areiras, P. M. A., Belytchko, T., 2006. A method for dynamic crack and shear band propagation with phantom nodes. International Journal for Numerical Methods in Engineering 67, 868 – 893. Sumi, Y., 2014. Mathematical and Computational Analyses of Cracking Formation. Springer, Tokyo. Teng, Z. H., Sun, F., Wu, S. C., Zhang, Z. B., Chen, T., Liao, D. M., 2018. An adaptively refined XFEM with virtual node polygonal elements for dynamic crack problems. Computational Mechanics 62, 1087 – 1106. 5. Conclusions and generalizations Acknowledgements This research has been supported from the project of specific university research at Brno University of Technol ogy FAST-J-19-6018. References