Skip to main content
SpringerLink
Log in

A Concurrent Multiscale Method for Simulation of Crack Propagation

  • Published:
Acta Mechanica Solida Sinica Aims and scope Submit manuscript

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  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. 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.

    Article  MathSciNet  MATH  Google Scholar 

  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.

    Article  MathSciNet  MATH  Google Scholar 

  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.

    Article  MathSciNet  MATH  Google Scholar 

  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.

    Article  MathSciNet  MATH  Google Scholar 

  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.

    Article  MathSciNet  MATH  Google Scholar 

  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.

    Article  MathSciNet  MATH  Google Scholar 

  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.

    Article  MATH  Google Scholar 

  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.

    Article  MathSciNet  MATH  Google Scholar 

  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.

    Article  MATH  Google Scholar 

  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.

    Article  MATH  Google Scholar 

  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.

    Article  MathSciNet  MATH  Google Scholar 

  13. Belytschko, T. and Song, J.H., Coarse-graining of multiscale crack propagation. International Journal for Numerical Methods in Engineering, 2010, 81: 537–563.

    MATH  Google Scholar 

  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.

    Article  MathSciNet  MATH  Google Scholar 

  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.

    Article  MathSciNet  MATH  Google Scholar 

  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.

    Article  MathSciNet  MATH  Google Scholar 

  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.

    MATH  Google Scholar 

  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.

    Article  MathSciNet  MATH  Google Scholar 

  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.

    Article  MathSciNet  MATH  Google Scholar 

  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.

    Article  MathSciNet  MATH  Google Scholar 

  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.

    Article  MathSciNet  MATH  Google Scholar 

  22. Hou, T.Y., Multiscale modelling and computation of fluid flow. International Journal for Numerical Methods in Fluids, 2005, 47: 707–719.

    Article  MathSciNet  MATH  Google Scholar 

  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.

    Article  MATH  Google Scholar 

  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.

    Article  MATH  Google Scholar 

  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.

    Article  MATH  Google Scholar 

  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.

    Article  MathSciNet  MATH  Google Scholar 

  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.

    Article  Google Scholar 

  28. Abdelaziz, Y. and Hamouine, A., A survey of the extended finite element. Computers and structures, 2008, 86: 1141–1151.

    Article  Google Scholar 

  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.

    MathSciNet  MATH  Google Scholar 

  30. Pais, M., MATLAB Extended Finite Element (MXFEM) Code, Version 1.2, 2010. (Available from: www.matthewpais.com. [Accessed on April 3, 2012]).

  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.

    Article  MATH  Google Scholar 

  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.

    Article  MATH  Google Scholar 

  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.

    Article  MathSciNet  MATH  Google Scholar 

  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.

    Article  MATH  Google Scholar 

  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.

    Article  MathSciNet  MATH  Google Scholar 

  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.

    Article  MathSciNet  MATH  Google Scholar 

  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.

    Article  MATH  Google Scholar 

  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.

    Article  MathSciNet  MATH  Google Scholar 

  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.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. State Key Laboratory of Structural Analysis for Industrial Equipment, Department of Engineering Mechanics, Faculty of Vehicle Engineering and Mechanics, Dalian University of Technology, 116024, Dalian, China

    Jingkai Wu, Hongwu Zhang & Yonggang Zheng

  2. Nanjing Research Institute of Electronics Technology, 210039, Nanjing, China

    Jingkai Wu

Authors
  1. Jingkai Wu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Hongwu Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Yonggang Zheng
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Hongwu Zhang.

Additional information

Project supported by the National Natural Science Foundation of China (Nos. 11232003, 11072051, 11272003 and 91315302), the 111 Project (No. B08014), the National Basic Research Program of China (Nos. 2010CB832704 and 2011CB013401), Program for New Century Excellent Talents in University (No. NCET-13-0088) and Ph.D.Programs Foundation of Ministry of Education of China (No. 20130041110050).

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Wu, J., Zhang, H. & Zheng, Y. A Concurrent Multiscale Method for Simulation of Crack Propagation. Acta Mech. Solida Sin. 28, 235–251 (2015). https://doi.org/10.1016/S0894-9166(15)30011-2

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1016/S0894-9166(15)30011-2

Key Words

Search

Navigation