Acta Mechanica Solida Sinica

, Volume 28, Issue 3, pp 235–251 | Cite as

A Concurrent Multiscale Method for Simulation of Crack Propagation

Article

Abstract

A concurrent multiscale method is developed for simulating quasi-static crack propagation in which the failure processes occur in only a small portion of the structure. For this purpose, a multiscale model is adopted and both scales are discretized with finite-element meshes. The extended finite element method is employed to take into account the propagation of discontinuities on the fine-scale subregions. At the same time, for the other subregions, the coarse-scale mesh is employed and is resolved by using the extended multiscale finite element method. Several representative numerical examples are given to verify the validity of the method.

Key Words

concurrent multiscale method crack propagation extended finite element method level set method 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Babuška, I., Homogenization approach in engineering. In: Lions, J.L. and Glowinski, R. (Eds.), Computing Methods in Applied Science and Engineering, Lecture Note in Economics and Mathematical Systems. Berlin: Springer, 1976, 134: 137–153.Google Scholar
  2. 2.
    Guedes, J.M. and Kikuchi, N., Preprocessing and postprocessing for materials based on the homogenization method with adaptive finite element methods. Computer Methods in Applied Mechanics and Engineering, 1990, 83: 143–198.MathSciNetCrossRefMATHGoogle Scholar
  3. 3.
    Fish, J., Shek, K., Pandheeradi, M. and Shephard, M., Computational plasticity for composite structures based on mathematical homogenization: theory and practice. Computer Methods in Applied Mechanics and Engineering, 1997, 148: 53–73.MathSciNetCrossRefMATHGoogle Scholar
  4. 4.
    Hughes, T.J.R., Multiscale phenomena: Green’s function, the Dirichlet-to-Neumann formulation, subgrid scale models, bubbles and the origins of stabilized method. Computer Methods in Applied Mechanics and Engineering, 1995, 127: 387–401.MathSciNetCrossRefMATHGoogle Scholar
  5. 5.
    Hughes, T.J.R., Feijoo, G.R., Mazzei, L. and Quincy, J.B., The variational multiscale method-a paradigm for computational mechanics. Computer Methods in Applied Mechanics and Engineering, 1998, 166: 3–24.MathSciNetCrossRefMATHGoogle Scholar
  6. 6.
    Garikipati, K. and Hughes, T.J.R., A study of strain localization in a multiple scale framework–the one-dimensional problem. Computer Methods in Applied Mechanics and Engineering, 2000, 159: 193–222.MathSciNetCrossRefMATHGoogle Scholar
  7. 7.
    Garikipati, K. and Hughes, T.J.R., A variational multiscale approach to strain localization-formulation for multidimensional problems. Computer Methods in Applied Mechanics and Engineering, 2000, 188: 39–60.MathSciNetCrossRefMATHGoogle Scholar
  8. 8.
    Yeon, J.H. and Youn, S.K., Meshfree analysis of softening elastoplastic solids using variational multiscale method. International Journal of Solids and Structures, 2005, 42: 4030–4057.CrossRefMATHGoogle Scholar
  9. 9.
    Mergheim, J., A variational multiscale method to model crack propagation at finite strains. International Journal for Numerical Methods in Engineering, 2009, 80: 269–289.MathSciNetCrossRefMATHGoogle Scholar
  10. 10.
    Hettich, T., Hund, A. and Ramm, E., Modeling of failure in composites by X-FEM and level sets within a multiscale framework. Computer Methods in Applied Mechanics and Engineering, 2008, 197: 414–424.CrossRefMATHGoogle Scholar
  11. 11.
    Guidault, P.A., Allix, O., Champaney, L. and Cornuault, C., A multiscale extended finite element method for crack propagation. Computer Methods in Applied Mechanics and Engineering, 2008, 197: 381–399.CrossRefMATHGoogle Scholar
  12. 12.
    Loehnert, S. and Belytschko, T., A multiscale projection method for macro/microcrack simulations. International Journal for Numerical Methods in Engineering, 2007, 71: 1466–1482.MathSciNetCrossRefMATHGoogle Scholar
  13. 13.
    Belytschko, T. and Song, J.H., Coarse-graining of multiscale crack propagation. International Journal for Numerical Methods in Engineering, 2010, 81: 537–563.MATHGoogle Scholar
  14. 14.
    Pereira, J.P.A., Kim, D.J. and Duarte, C.A., A two-scale approach for the analysis of propagating three-dimensional fractures. Computational Mechanics, 2012, 49: 99–121.MathSciNetCrossRefMATHGoogle Scholar
  15. 15.
    Pierres, E., Baietto, M.C. and Gravouil, A., A two-scale extended finite element method for modelling 3D crack growth with interfacial contact. Computer Methods in Applied Mechanics and Engineering, 2010, 199: 1165–1177.MathSciNetCrossRefMATHGoogle Scholar
  16. 16.
    Holl, M., Loehnert, S. and Wriggers, P., An adaptive multiscale method for crack propagation and crack coalescence. International Journal for Numerical Methods in Engineering, 2013, 93: 23–51.MathSciNetCrossRefMATHGoogle Scholar
  17. 17.
    Kim, D.J., Pereira, J. P. and Duarte, C.A., Analysis of three-dimensional fracture mechanics problems: a two-scale approach using coarse-generalized FEM meshes. International Journal for Numerical Methods in Engineering, 2010, 81: 335–365.MATHGoogle Scholar
  18. 18.
    Lian, W.D., Legrain, G. and Cartraud, P., Image-based computational homogenization and localization: comparison between X-FEM/levelset and voxel-based approaches. Computational Mechanics, 2013, 51: 279–293.MathSciNetCrossRefMATHGoogle Scholar
  19. 19.
    Zhang, H.W., Wu, J.K. and Fu, Z.D., A new multiscale computational method for elasto-plastic analysis of heterogeneous materials. Computational Mechanics, 2012, 49: 149–169.MathSciNetCrossRefMATHGoogle Scholar
  20. 20.
    Zhang, H.W., Liu, H. and Wu, J.K., A uniform multiscale method for 2D static and dynamic analyses of heterogeneous materials. International Journal for Numerical Methods in Engineering, 2013, 93: 714–746.MathSciNetCrossRefMATHGoogle Scholar
  21. 21.
    Hou, T.Y. and Wu, X.H., A multiscale finite element method for elliptic problems in composite materials and porous media. Journal of Computational Physics, 1997, 134: 169–89.MathSciNetCrossRefMATHGoogle Scholar
  22. 22.
    Hou, T.Y., Multiscale modelling and computation of fluid flow. International Journal for Numerical Methods in Fluids, 2005, 47: 707–719.MathSciNetCrossRefMATHGoogle Scholar
  23. 23.
    Belytschko, T. and Black, T., Elastic crack growth in finite elements with minimal remeshing. International Journal for Numerical Methods in Engineering, 1999, 45: 601–620.CrossRefMATHGoogle Scholar
  24. 24.
    Moes, N., Dolbow, J. and Belytschko, T., A finite element method for crack growth without remeshing. International Journal for Numerical Methods in Engineering, 1999, 46: 131–150.CrossRefMATHGoogle Scholar
  25. 25.
    Stolarska, M., Chopp, D.L., Moes, N. and Belyschko, T., Modelling crack growth by level sets in the extended finite element method. International Journal for Numerical Methods in Engineering, 2001, 51: 943–960.CrossRefMATHGoogle Scholar
  26. 26.
    Sukumar, N., Chopp, D., Moes, N. and Belytschko, T., Modeling holes and inclusions by level sets in the extended finite-element method. Computer Methods in Applied Mechanics and Engineering, 2001, 190: 6183–6200.MathSciNetCrossRefMATHGoogle Scholar
  27. 27.
    Karihaloo, B.L. and Xiao, Q.Z., Modelling of stationary and growing cracks in FE framework without remeshing: a state-of-the-art review. Computers and Structures, 2003, 81: 119–129.CrossRefGoogle Scholar
  28. 28.
    Abdelaziz, Y. and Hamouine, A., A survey of the extended finite element. Computers and structures, 2008, 86: 1141–1151.CrossRefGoogle Scholar
  29. 29.
    Fries, T.P. and Belytschko, T., The extended/generalized finite element method: An overview of the method and its applications. International Journal for Numerical Methods in Engineering, 2010, 84: 253–304.MathSciNetMATHGoogle Scholar
  30. 30.
    Pais, M., MATLAB Extended Finite Element (MXFEM) Code, Version 1.2, 2010. (Available from: www.matthewpais.com. [Accessed on April 3, 2012]).
  31. 31.
    Sukumar, N. and Prevost, J.H., Modeling quasi-static crack growth with the extended finite element method part i: computer implementation. International Journal of Solids and Structures, 2003, 40: 7513–7537.CrossRefMATHGoogle Scholar
  32. 32.
    Bordas, S., Nguyen, P.V., Dunant, C., Guidoum, A. and Nguyen-Dang, H., An extended finite element library. International Journal for Numerical Methods in Engineering, 2007, 71: 703–732.CrossRefMATHGoogle Scholar
  33. 33.
    Melenk, J.M. and Babuska, I., The partition of unity finite element method: basic theory and applications. Computer Methods in Applied Mechanics and Engineering, 1996, 139: 289–314.MathSciNetCrossRefMATHGoogle Scholar
  34. 34.
    Belytschko, T., Moes, N., Usui, S. and Parimi, C., Arbitrary discontinuities in finite elements. International Journal for Numerical Methods in Engineering, 2001, 50: 993–1013.CrossRefMATHGoogle Scholar
  35. 35.
    Legay, A., Wang, H.W. and Belytschko, T., Strong and weak arbitrary discontinuities in spectral finite elements. International Journal for Numerical Methods in Engineering, 2005, 64: 991–1008.MathSciNetCrossRefMATHGoogle Scholar
  36. 36.
    Fries, T.P., A corrected XFEM approximation without problems in blending elements. International Journal for Numerical Methods in Engineering, 2008, 75(5): 503–532.MathSciNetCrossRefMATHGoogle Scholar
  37. 37.
    Moes, N., Cloirec, M., Cartraud, P. and Remacle, J., A computational approach to handle complex microstructure geometries. Computer Methods in Applied Mechanics and Engineering, 2003, 192: 3163–3177.CrossRefMATHGoogle Scholar
  38. 38.
    Osher, S. and Sethian, J., Fronts propagating with curvature dependent speed: Algorithms based on Hamilton-Jacobi formulations. Journal of Computational Physics, 1988, 79: 12–49.MathSciNetCrossRefMATHGoogle Scholar
  39. 39.
    Erdogan, F. and Sih, G.C., On the crack extension in plates under plane loading and transverse shear. Transactions of the ASME. Journal of Basic Engineering, 1963, 85: 519–525.CrossRefGoogle Scholar

Copyright information

© The Chinese Society of Theoretical and Applied Mechanics and Technology 2015

Authors and Affiliations

  1. 1.State Key Laboratory of Structural Analysis for Industrial Equipment, Department of Engineering Mechanics, Faculty of Vehicle Engineering and MechanicsDalian University of TechnologyDalianChina
  2. 2.Nanjing Research Institute of Electronics TechnologyNanjingChina

Personalised recommendations