Skip to main content
SpringerLink
Log in

Image-based computational homogenization and localization: comparison between X-FEM/levelset and voxel-based approaches

  • Original Paper
  • Published:
Computational Mechanics Aims and scope Submit manuscript

Abstract

In material science, images are increasingly used as input data for computational models. In most of the published papers, voxel-based finite element models are employed using a mesh that is automatically built by converting each voxel into a finite element. We have recently proposed (Legrain et al., Int J Numer Methods Eng 86(7): 915–934, 2011) another computational approach for incorporating images in models, based on the extended finite element method (X-FEM) and levelsets. Its main advantages are that the mesh does not need to conform to the geometry and that a smooth representation of physical surfaces is obtained. The aim of this paper is to compare the two approaches in the framework of computational homogenization in elasticity, starting from material microstructural images. Attention will be paid to geometrical approximations, macroscopic properties and local quantities (e.g. stress oscillations, local error etc.). It is shown that the X-FEM/levelset approach is more efficient than voxel-based FEM.

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. Arbenz P, Flaig C (2008) On smoothing surfaces in voxel based finite element analysis of trabecular bone. Lect Notes Comput Sci 4818(1): 69

    Article  MathSciNet  Google Scholar 

  2. Belytschko T, Black T (1999) Elastic crack growth in finite elements with minimal remeshing. Int J Numer Methods Eng 45(5): 601–620

    Article  MathSciNet  MATH  Google Scholar 

  3. Belytschko T, Parimi C, Moës N, Sukumar N, Usui S (2003) Structured extended finite element methods for solids defined by implicit surfaces. Int J Numer Methods Eng 56(4): 609–635

    Article  MATH  Google Scholar 

  4. Boyd S, Müller R (2006) Smooth surface meshing for automated finite element model generation from 3D image data. J Biomech 39(7): 1287–1295

    Article  Google Scholar 

  5. Camacho D, Hopper R, Lin G, Myers B (1997) An improved method for finite element mesh generation of geometrically complex structures with application to the skullbase. J Biomech 30(10): 1067–1070

    Article  Google Scholar 

  6. Cebral J, Löhner R (2001) From medical images to anatomically accurate finite element grids. Int J Numer Methods Eng 51(8): 985–1008

    Article  MATH  Google Scholar 

  7. Charras GT, Guldberg RE (2000) Improving the local solution accuracy of large-scale digital image-based finite element analyses. J Biomech 33(2): 255–259

    Article  Google Scholar 

  8. Dréau K, Chevaugeon N, Moës N (2010) Studied X-FEM enrichment to handle material interfaces with higher order finite element. Comput Methods Appl Mech Eng 199(29-32): 1922–1936

    Article  MATH  Google Scholar 

  9. Frey P (2004) Generation and adaptation of computational surface meshes from discrete anatomical data. Int J Numer Methods Eng 60(6): 1049–1074

    Article  MATH  Google Scholar 

  10. Frey P, George PL (2000) Mesh generation: application to finite elements. Hermes Science Europe Ltd., UK

    MATH  Google Scholar 

  11. Fries TP, Belytschko T (2010) The extended/generalized finite element method: an overview of the method and its applications. Int J Numer Methods Eng 84(3): 253–304

    MathSciNet  MATH  Google Scholar 

  12. Gitman I, Askes H, Sluys L (2007) Representative volume: existence and size determination. Eng Fract Mech 74(16): 2518–2534

    Article  Google Scholar 

  13. Golanski D, Terada K, Kikuchi N (1997) Macro and micro scale modeling of thermal residual stresses in metal matrix composite surface layers by the homogenization method. Comput Mech 19(3): 188–202

    Article  Google Scholar 

  14. Guessasma S, Chaunier L, Della Valle G, Lourdin D (2011) Mechanical modelling of cereal solid foods. Trends Food Sci Technol 22(4): 142–153

    Article  Google Scholar 

  15. Guldberg RE, Hollister SJ, Charras GT (1998) The accuracy of digital image-based finite element models. J Biomech Eng 120(2): 289–295

    Article  Google Scholar 

  16. Hollister SJ, Kikuchi N (1994) Homogenization theory and digital imaging: a basis for studying the mechanics and design principles of bone tissue. Biotechnol Bioeng 43(7): 586–596

    Article  Google Scholar 

  17. Ibanez L, Schroeder W, Ng L, Cates J (2005) The ITK Software Guide, 2nd edn. Kitware, Inc. ISBN 1-930934-15-7, http://www.itk.org/ItkSoftwareGuide.pdf

  18. Jiang M, Jasiuk I, Ostoja-Starzewski M (2002) Apparent elastic and elastoplastic behavior of periodic composites. Int J Solids Struct 39(1): 199–212

    Article  MATH  Google Scholar 

  19. Kanit T, Forest S, Galliet I, Mounoury V, Jeulin D (2003) Determination of the size of the representative volume element for random composites: statistical and numerical approach. Int J Solids Struct 40(13-14): 3647–3679

    Article  MATH  Google Scholar 

  20. Kanit T, Nguyen F, Forest S, Jeulin D, Reed M, Singleton S (2006) Apparent and effective physical properties of heterogeneous materials: Representativity of samples of two materials from food industry. Comput Methods Appl Mech Eng 195(33–36): 3960–3982

    Article  MATH  Google Scholar 

  21. Keyak J, Meagher J, Skinner H, Motejr C (1990) Automated three-dimensional finite element modelling of bone: a new method. J Biomed Eng 12(5): 389–397

    Article  Google Scholar 

  22. Legrain G, Cartraud P, Perreard I, Moës N (2011) An X-FEM and level set computational approach for image-based modelling: application to homogenization. Int J Numer Methods Eng 86(7): 915–934

    Article  MATH  Google Scholar 

  23. Legrain G, Chevaugeon N, Dréau K (2011) High order extended finite element method and level sets: uncoupling geometry and approximation. In: ECCOMAS XFEM 2011 Conference, Cardiff

  24. Legrain G, Chevaugeon N, Dréau K (2012) High order X-FEM and levelsets for complex microstructures: uncoupling geometry and approximation. Submitted to: Comput Methods Appl Mech Eng

  25. Maire E, Fazekas A, Salvo L, Dendievel R, Youssef S, Cloetens P, Letang J (2003) X-ray tomography applied to the characterization of cellular materials. Related finite element modeling problems. Compos Sci Technol 63(16): 2431–2443

    Article  Google Scholar 

  26. Melenk J, Babuška I (1996) The partition of unity finite element method: basic theory and applications. Comput Methods Appl Mech Eng 139(1-4): 289–314

    Article  MATH  Google Scholar 

  27. Michel J, Moulinec H, Suquet P (1999) Effective properties of composite materials with periodic microstructure: a computational approach. Comput Methods Appl Mech Eng 172(1-4): 109–143

    Article  MathSciNet  MATH  Google Scholar 

  28. Mishnaevsky L (2005) Automatic voxel-based generation of 3D microstructural FE models and its application to the damage analysis of composites. Mater Sci Eng A-Struct 407(1-2): 11–23

    Article  Google Scholar 

  29. Moës N, Cloirec M, Cartraud P, Remacle J (2003) A computational approach to handle complex microstructure geometries. Comput Methods Appl Mech Eng 192(28-30): 3163–3177

    Article  MATH  Google Scholar 

  30. Osher S, Sethian J (1988) Fronts propagations with curvature dependent speed: algorithms based on Hamilton-Jacobi formulations. J Comput Phys 79: 12–49

    Article  MathSciNet  MATH  Google Scholar 

  31. Ostoja-Starzewski M (2008) Microstructural randomness and scaling in mechanics of materials. Chapman and Hall/CRC, Florida

    MATH  Google Scholar 

  32. Sakellariou A, Arns C, Sheppard A, Sok R, Averdunk H, Limaye A, Jones A, Senden T, Knackstedt M (2007) Developing a virtual materials laboratory. Mater Today 10(12): 44–51

    Article  Google Scholar 

  33. Sethian J (1999) Level set methods and fast marching methods evolving interfaces in computational geometry, fluid mechanics, computer vision, and materials science, 2nd edn

  34. Still M (2006) The definitive guide to ImageMagick—learn how to use the open source ImageMagick program to transform images, 1st edn. Apress

  35. Stolarska M, Chopp DL, Moës N, Belytschko T (2001) Modelling crack growth by level sets and the extended finite element method. Int J Numer Methods Eng 51(8):943–960

    Google Scholar 

  36. Sukumar N, Chopp D, Moës NT (2001) Modeling holes and inclusions by level sets in the extended finite-element method. Comput Methods Appl Mech Eng 190(46-47): 6183–6200

    Article  MATH  Google Scholar 

  37. Terada K, Miura T, Kikuchi N (1997) Digital image-based modeling applied to the homogenization analysis of composite materials. Comput Mech 20: 331–346

    Article  MATH  Google Scholar 

  38. Tran AB, Yvonnet J, He QC, Toulemonde C, Sanahuja J (2011) A multiple level set approach to prevent numerical artefacts in complex microstructures with nearby inclusions within XFEM. Int J Numer Methods Eng 85(11): 1436–1459

    Article  MATH  Google Scholar 

  39. Ulrich D, Van Rietbergen B, Weinans H, Rüegsegger P (1998) Finite element analysis of trabecular bone structure: a comparison of image-based meshing techniques. J Biomech 31(12): 1187–1192

    Article  Google Scholar 

  40. Vese L, Chan T (2002) A multiphase level set framework for image segmentation using the Mumford and Shah model. Int J Comput Vision 50(3): 271–293

    Article  MATH  Google Scholar 

  41. Viceconti M, Bellingeri L, Cristofolini L, Toni A (1998) A comparative study on different methods of automatic mesh generation of human femurs. Med Eng Phys 20(1): 1–10

    Article  Google Scholar 

  42. Wang ZL, Teo JCM, Chui CK, Ong SH, Yan CH, Wang SC, Wong HK, Teoh SH (2005) Computational biomechanical modelling of the lumbar spine using marching-cubes surface smoothened finite element voxel meshing. Comput Methods Programs Biomed 80(1): 25–35

    Article  Google Scholar 

  43. Young PG, Beresford-West TBH, Coward SRL, Notarberardino B, Walker B, Abdul-Aziz A (2008) An efficient approach to converting three-dimensional image data into highly accurate computational models. Philos Trans A Math Phys Eng Sci 366(1878): 3155–3173

    Article  MathSciNet  Google Scholar 

  44. Yvonnet J, He QC, Toulemonde C (2008a) Numerical modelling of the effective conductivities of composites with arbitrarily shaped inclusions and highly conducting interface. Compos Sci Technol 68(13): 2818–2825

    Article  Google Scholar 

  45. Yvonnet J, Quang H, He Q (2008b) An xfem/level set approach to modelling surface/interface effects and to computing the size-dependent effective properties of nanocomposites. Comput Mech 42: 119–131

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. LUNAM Université, GeM, UMR CNRS 6183, Ecole Centrale de Nantes, 1 rue de la Noë, 44 321, Nantes Cédex 3, France

    W. D. Lian, G. Legrain & P. Cartraud

Authors
  1. W. D. Lian
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. G. Legrain
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. P. Cartraud
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to P. Cartraud.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Lian, W.D., Legrain, G. & Cartraud, P. Image-based computational homogenization and localization: comparison between X-FEM/levelset and voxel-based approaches. Comput Mech 51, 279–293 (2013). https://doi.org/10.1007/s00466-012-0723-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00466-012-0723-9

Keywords

Search

Navigation