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Multiscale simulation of major crack/minor cracks interplay with the corrected XFEM

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Języki publikacji
EN
Abstrakty
EN
The present work aims at saving computational cost of multiscale simulation on major crack/minor crack interaction problems. The multiscale extended finite element method (MsXFEM) used for the numerical simulation is developed on multiscale projection technique which enables different scale decomposition, and transition of field variables between different scales. Both macroscale and microscale problems are solved independently and alternatively, in the framework of XFEM. The improvement made in this paper is to employ corrected XFEM on the macroscale level, so that a more accurate boundary condition can be obtained for the microscale problem. The modification leads to a reduced necessary microscale domain size, meanwhile a solution of higher accuracy and enhanced convergence rate can be achieved. The numerical examples of minor cracks near a major one are studied, which show that the effect of minor cracks on major crack can be efficiently captured.
Rocznik
Strony
410--418
Opis fizyczny
Bibliogr. 34 poz., rys., tab., wykr.
Twórcy
autor
  • Department of Civil Engineering, School of Naval Architecture, Ocean and Civil Engineering, Shanghai Jiao Tong University, No. 800, Dongchuan Road, Shanghai 200240, China
autor
  • Department of Civil Engineering, School of Naval Architecture, Ocean and Civil Engineering, Shanghai Jiao Tong University, No. 800, Dongchuan Road, Shanghai 200240, China
  • State Key Laboratory of Ocean Engineering, Shanghai Jiao Tong University, No. 800, Dongchuan Road, Shanghai 200240, China
  • Collaborative Innovation Center for Advanced Ship and Deep-Sea Exploration, No. 800, Dongchuan Road, Shanghai 200240, China
autor
  • Department of Civil Engineering, School of Naval Architecture, Ocean and Civil Engineering, Shanghai Jiao Tong University, No. 800, Dongchuan Road, Shanghai 200240, China
autor
  • Department of Civil Engineering, School of Naval Architecture, Ocean and Civil Engineering, Shanghai Jiao Tong University, No. 800, Dongchuan Road, Shanghai 200240, China
autor
  • Department of Civil Engineering, School of Naval Architecture, Ocean and Civil Engineering, Shanghai Jiao Tong University, No. 800, Dongchuan Road, Shanghai 200240, China
  • Cullen College of Engineering, University of Houston, Houston, TX 77204, USA
Bibliografia
  • [1] R.B. Bai, M. Radzieński, M.S. Cao, W. Ostachowicz, et al., Non-baseline identification of delamination in plates using wavelet aided fractal analysis of two dimensional mode shapes, Journal of Intelligent Material Systems and Structures 26 (17) (2015) 2338–2350.
  • [2] R.B. Bai, X.G. Song, M. Radzieński, M.S. Cao, et al., Crack location in beams by data fusion of fractal dimension features of laser-measured operating deflection shapes, Smart Structures and Systems 13 (6) (2014) 975–991.
  • [3] I. Hirai, B. Wang, W.D. Pilkey, An exact zooming method, Finite Elements in Analysis and Design 1 (1) (1985).
  • [4] M. Kikuchi, Y. Wada, Y. Shintaku, K. Suga, et al., Fatigue crack growth simulation in heterogeneous material using s-version FEM, International Journal of Fatigue 58 (2014) 47–55.
  • [5] J. Fish, K. Shek, M. Pandheeradi, M.S. Shephard, Computational plasticity for composite structures based on mathematical homogenization: theory and practice, Computer Methods in Applied Mechanics and Engineering 148 (1–2) (1997) 53–73.
  • [6] E. Svenning, M. Fagerström, F. Larsson, Computational homogenization of microfractured continua using weakly periodic boundary conditions, Computer Methods in Applied Mechanics and Engineering 299 (2016) 1–21.
  • [7] T.J.R. Hughes, Multiscale phenomena: Green's functions, the Dirichlet-to-Neumann formulation, subgrid scale models, bubbles and the origins of stabilized methods, Computer Methods in Applied Mechanics and Engineering 127 (1–4) (1995) 387–401.
  • [8] X. Bian, Z. Li, G.E. Karniadakis, Multi-resolution flow simulations by smoothed particle hydrodynamics via domain decomposition, Journal of Computational Physics 297 (2015) 132–155.
  • [9] F. Greco, L. Leonetti, P. Lonetti, P. Nevone Blasi, Crack propagation analysis in composite materials by using moving mesh and multiscale techniques, Computers & Structures 153 (2015) 201–216.
  • [10] J. Wu, H. Zhang, Y. Zheng, A concurrent multiscale method for simulation of crack propagation, Acta Mechanica Solida Sinica 28 (3) (2015) 235–251.
  • [11] R. Gracie, T. Belytschko, Concurrently coupled atomistic and XFEM models for dislocations and cracks, International Journal for Numerical Methods in Engineering 78 (3) (2009) 354–378.
  • [12] S. Loehnert, A stabilization technique for the regularization of nearly singular extended finite elements, Computational Mechanics 54 (2) (2014) 523–533.
  • [13] S. Loehnert, T. Belytschko, A multiscale projection method for macro/microcrack simulations, International Journal for Numerical Methods in Engineering 71 (12) (2007) 1466–1482.
  • [14] X. Yan, A boundary element modeling of fatigue crack growth in a plane elastic plate, Mechanics Research Communications 33 (4) (2006) 470–481.
  • [15] E.D. Leonel, A. Chateauneuf, W.S. Venturini, Probabilistic crack growth analyses using a boundary element model: applications in linear elastic fracture and fatigue problems, Engineering Analysis with Boundary Elements 36 (6) (2012) 944–959.
  • [16] M. Duflot, H. Nguyen-Dang, Fatigue crack growth analysis by an enriched meshless method, Journal of Computational and Applied Mathematics 168 (1–2) (2004) 155–164.
  • [17] K.Y. Dai, G.R. Liu, X. Han, K.M. Lim, Thermomechanical analysis of functionally graded material (FGM) plates using element-free Galerkin method, Computers & Structures 83 (17–18) (2005) 1487–1502.
  • [18] Y. Tal, Y.H. Hatzor, X. Feng, An improved numerical manifold method for simulation of sequential excavation in fractured rocks, International Journal of Rock Mechanics and Mining Sciences 65 (2014) 116–128.
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  • [20] N. Moës, J. Dolbow, T. Belytschko, A finite element method for crack growth without remeshing, International Journal for Numerical Methods in Engineering 46 (1999) 131–150.
  • [21] T.T. Yu, Z.W. Gong, Numerical simulation of temperature field in heterogeneous material with the XFEM, Archives of Civil and Mechanical Engineering 13 (2) (2013) 199–208.
  • [22] É. Budyn, G. Zi, N. Moës, T. Belytschko, A method for multiple crack growth in brittle materials without remeshing, International Journal for Numerical Methods in Engineering 61 (10) (2004) 1741–1770.
  • [23] P.A. Guidault, O. Allix, L. Champaney, J.P. Navarro, A micro-macro approach for crack propagation with local enrichment, in: Proceedings of the Seventh International Conference on Computational Structures Technology, Scotland, 2004.
  • [24] I.V. Singh, B.K. Mishra, S. Bhattacharya, XFEM simulation of cracks, holes and inclusions in functionally graded materials, International Journal of Mechanics and Materials in Design 7 (3) (2011) 199–218.
  • [25] P.A. Guidault, O. Allix, L. Champaney, C. Cornuault, A multiscale extended finite element method for crack propagation, Computer Methods in Applied Mechanics and Engineering 197 (5) (2008) 381–399.
  • [26] E. Bosco, V.G. Kouznetsova, M.G.D. Geers, Multi-scale computational homogenization-localization for propagating discontinuities using X-FEM, International Journal for Numerical Methods in Engineering 102 (3–4) (2015) 496–527.
  • [27] J. Chessa, H. Wang, T. Belytschko, On the construction of blending elements for local partition of unity enriched finite elements, International Journal for Numerical Methods in Engineering 57 (7) (2003) 1015–1038.
  • [28] J. Wu, F. Li, An improved stable XFEM (Is-XFEM) with a novel enrichment function for the computational modeling of cohesive cracks, Computer Methods in Applied Mechanics and Engineering 295 (2015) 77–107.
  • [29] T.P. Fries, A corrected XFEM approximation without problems in blending elements, International Journal for Numerical Methods in Engineering 75 (5) (2008) 503–532.
  • [30] T.T. Yu, The extended finite element method (XFEM) for discontinuous rock masses, Engineering Computations 28 (3) (2011) 634–659.
  • [31] Q.Z. Xiao, B.L. Karihaloo, Improving the accuracy of XFEM crack tip fields using higher order quadrature and statically admissible stress recovery, International Journal for Numerical Methods in Engineering 66 (9) (2006) 1378–1410.
  • [32] I.V. Singh, G. Bhardwaj, B.K. Mishra, A new criterion for modeling multiple discontinuities passing through an element using XIGA, Journal of Mechanical Science and Technology 29 (3) (2015) 1131–1143.
  • [33] S.X. Gong, H. Horii, General solution to the problem of microcracks near the tip of a main crack, Journal of the Mechanics and Physics of Solids 1 (37) (1989) 27–46.
  • [34] S.A. Meguid, P.E. Gaultier, S.X. Gong, A comparison between analytical and finite element analysis of main crack-microcrack interaction, Engineering Fracture Mechanics 6 (38) (1991) 451–465.
Uwagi
PL
Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę (zadania 2017)
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-5bd62ead-e6ac-4f60-9061-54af1b8b59d9
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