International Journal of Material Forming

, Volume 10, Issue 4, pp 567–580 | Cite as

BEM computation of 3D Stokes flow including moving front

  • M.-Q. Thai
  • F. Schmidt
  • G. Dusserre
  • A. Cantarel
  • L. Silva
Original Research


Liquid composite molding (LCM) includes all composite-manufacturing methods, where the liquid state resin is forced into the dry preformed reinforcement. In this study, numerical simulation of the resin infusion is presented based on a coupled approach involving Boundary Element Method (BEM) and Level Set Method. The method developed can handle stationary and transient flows by solving the Stokes equations. The numerical results on a square packed set of fibers show excellent agreement with the analytical model. The comparison between experimental and simulation results of flow front patterns revealed a fair accordance.


Liquid composite molding Boundary element method Level set Resin flow 



This work was carried out in the framework of the collaborative French project “De l’image au maillage” coordinated by Mines Telecom Institute (IMT). The authors gratefully acknowledge S. Leroux for her contribution to this work. Author Minh-Quan THAI has received research grants from the Vietnam National Foundation for Science and Technology Development (NAFOSTED) under grant number 107.02-2015.17. The other authors declare that they have no conflict of interest.


  1. 1.
    Beukers A (2001) Polymer matrix composites : applications. Encyclopedia of Materials : Science and Technology. Elsevier, Oxford. p 7384–7388Google Scholar
  2. 2.
    Jones RM (1998) Mechanics of composite materials. CRC PressGoogle Scholar
  3. 3.
    Gantois R (2012) Contribution à la modélisation de l’écoulement de résine dans les procédés de moulage des composites par voie liquide. In Thesis. Université de ToulouseGoogle Scholar
  4. 4.
    Patel N, Lee LJ (1995) Effects of fiber mat architecture on void formation and removal in liquid composite molding. Polym Compos 16(5):386–399CrossRefGoogle Scholar
  5. 5.
    Rouison D, Sain M, Couturier M (2004) Resin transfer molding of natural fiber reinforced composites: cure simulation. Compos Sci Technol 64(5):629–644CrossRefGoogle Scholar
  6. 6.
    Gantois R, Cantarel A, Dusserre G, Félices JN, Schmidt F (2010) Numerical simulation of resin transfer molding using BEM and level set method. Int J Mater Form 3(1):635–638CrossRefGoogle Scholar
  7. 7.
    Silva L, Puaux G, Vincent M, Laure P. A monolithic finite element approach to compute permeabilityatc microscopic scales in LCM processes. Int J Mater Form 3(1):619–622Google Scholar
  8. 8.
    Chen X, Papathanasiou TD (2007) Micro-scale modeling of axial flow through unidirectional disordered fiber arrays. Compos Sci Technol 67:1286–1293CrossRefGoogle Scholar
  9. 9.
    Brebbia CA, Dominguez J (1992) Boundary elements: an introductory course. Computational Mechanics Publications, 2nd editionGoogle Scholar
  10. 10.
    Paris F, Canas J (1997) Boundary element method : fundamentals and applications. Oxford University PressGoogle Scholar
  11. 11.
    Osher S, Sethian JA (1988) Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations. J Comput Phys 79(1):12–49MathSciNetCrossRefzbMATHGoogle Scholar
  12. 12.
    Sethian JA (1999) Level set methods and fast marching methods evolving interfaces in computational geometry, fluid mechanics, computer vision, and materials science. Cambridge University Press, 2e éditionGoogle Scholar
  13. 13.
    Liu Y, Moulin N, Bruchon J, Liotier P-J, Drapier S (2016) Towards void formation and permeability predictions in LCM processes: a computational bifluid–solid mechanics framework dealing with capillarity and wetting issues. Comptes Rendus Mécanique 344(4–5):236–250CrossRefGoogle Scholar
  14. 14.
    Abouorm L, Moulin N, Bruchon J, Drapier S (2013) Monolithic approach of Stokes-Darcy coupling for LCM process modelling. Current state-of-the-art on material forming: numerical and experimental approaches at different length-scales, PTS 1–3. 554–557:447–455Google Scholar
  15. 15.
    Trochu F, Ruiz E, Achim V, Soukane S (2006) Advanced numerical simulation of liquid composite molding for process analysis and optimization. Compos A: Appl Sci Manuf 37(6):890–902CrossRefGoogle Scholar
  16. 16.
    Colicchio G, Greco M, Faltinsen OM (2006) A BEM-level set domain-decomposition strategy for non-linear and fragmented interfacial flows. Vol. 67. Chichester, ROYAUME-UNI: Wiley. 1385–1419Google Scholar
  17. 17.
    Garzon M, Adalsteinsson D, Gray L, Sethian JA (2005) A coupled level set-boundary integral method for moving boundary simulations. Interfaces Free Boundaries 7(3):277–302MathSciNetCrossRefzbMATHGoogle Scholar
  18. 18.
    Gantois R, Cantarel A, Cosson B, Dusserre G, Felices J-N, Schmidt F (2013) BEM-based models to simulate the resin flow at macroscale and microscale in LCM processes. Polym Compos 34(8):1235–1244CrossRefGoogle Scholar
  19. 19.
    Soukane S, Trochu F (2006) Application of the level set method to the simulation of resin transfer molding. Compos Sci Technol 66(7–8):1067–1080CrossRefGoogle Scholar
  20. 20.
    Gebart BR (1992) Permeability of unidirectional reinforcements for RTM. J Compos Mater 26:1100–1133CrossRefGoogle Scholar
  21. 21.
    Berdichevsky AL, Cai Z (1993) Preform permeability predictions by self-consistent method and finite element simulation. Polym Compos 14(2):132–143CrossRefGoogle Scholar
  22. 22.
    Dusserre G, Jourdain E, Bernhart G. Effect of deformation on knitted glass preform in-plane permeability. Polym Compos 32(1): 18–28Google Scholar
  23. 23.
    Sharma S (2010) On the improvement of permeability assessment of fibrous materials. In MS Aerospace engineering. Wichita State UniversityGoogle Scholar
  24. 24.
    Loix F, Orgéas L, Geindreau C, Badel P, Boisse P, Bloch JF (2009) Flow of non-Newtonian liquid polymers through deformed composites reinforcements. Compos Sci Technol 69(5):612–619CrossRefGoogle Scholar
  25. 25.
    Shirley P, Tuchman A (1990) A polygonal approximation to direct scalar volume rendering. SIGGRAPH Comput Graph 24(5):63–70CrossRefGoogle Scholar
  26. 26.
    Zheng X, Lowengrub J, Anderson A, Cristini V (2005) Adaptive unstructured volume remeshing – II: application to two- and three-dimensional level-set simulations of multiphase flow. J Comput Phys 208(2):626–650MathSciNetCrossRefzbMATHGoogle Scholar
  27. 27.
    Duysinx P, Van Miegroet L, Jacobs T, Fleury C (2006) Generalized shape optimization using X-FEM and level set methods. In: Bendsøe MP, Olhoff N, Sigmund O (eds) IUTAM symposium on topological design optimization of structures, machines and materials: status and perspectives. Springer Netherlands, Dordrecht, pp 23–32CrossRefGoogle Scholar
  28. 28.
    Divo E, Kassab A (1997) A generalized boundary-element method for steady-state heat conduction in heterogeneous anisotropic media. Numer Heat Transfer Part B: Fundam 32(1):37–61CrossRefzbMATHGoogle Scholar
  29. 29.
    Nerantzaki MS, Kandilas CB (2008) A boundary element method solution for anisotropic nonhomogeneous elasticity. Acta Mech 200(3):199–211CrossRefzbMATHGoogle Scholar
  30. 30.
    Gantois R, Cantarel A, Cosson B, Dusserre G, Felices J-N, Schmidt F. BEM-based models to simulate the resin flow at macroscale and microscale in LCM processes. Polym Compos 34(8): 1235–1244Google Scholar
  31. 31.
    Schmidt FM, Lafleur P, Berthet F, Devos P (1999) Numerical simulation of resin transfer molding using linear boundary element method. Polym Compos 20(6):725–732CrossRefGoogle Scholar
  32. 32.
    Hunter P, Pullan A (2003) FEM/BEM notes. Department of Engineering Science. University of Auckland, New ZealandGoogle Scholar
  33. 33.
    Fratantonio M, Rencis JJ (2000) Exact boundary element integrations for two-dimensional Laplace equation. Eng Anal Bound Elem 24(4):325–342CrossRefzbMATHGoogle Scholar
  34. 34.
    Telles FJC, Oliveira FR (1994) Third degree polynomial transformation for boundary element integrals: further improvements. Elsevier, Kidlington, Royaume-UniGoogle Scholar
  35. 35.
    Newman TS, Yi H (2006) A survey of the marching cubes algorithm. Comput Graph 30(5):854–879CrossRefGoogle Scholar
  36. 36.
    Oh S, Koo BK (2007) Data perturbation for fewer triangles in marching tetrahedra. Graph Model 69(3):211–218CrossRefGoogle Scholar
  37. 37.
    Sharma S, Siginer DA (2010) Permeability measurement methods in porous media of fiber reinforced composites. Appl Mech Rev 63(2):020802CrossRefGoogle Scholar
  38. 38.
    Arbter R, Beraud JM, Binetruy C, Bizet L, Bréard J, Comas-Cardona S, Demaria C, Endruweit A, Ermanni P, Gommer F, Hasanovic S, Henrat P, Klunker F, Laine B, Lavanchy S, Lomov SV, Long A, Michaud V, Morren G, Ruiz E, Sol H, Trochu F, Verleye B, Wietgrefe M, Wu W, Ziegmann G (2011) Experimental determination of the permeability of textiles: a benchmark exercise. Compos A: Appl Sci Manuf 42(9):1157–1168CrossRefGoogle Scholar
  39. 39.
    Vernet N, Ruiz E, Advani S, Alms JB, Aubert M, Barburski M, Barari B, Beraud JM, Berg DC, Correia N, Danzi M, Delavière T, Dickert M, Di Fratta C, Endruweit A, Ermanni P, Francucci G, Garcia JA, George A, Hahn C, Klunker F, Lomov SV, Long A, Louis B, Maldonado J, Meier R, Michaud V, Perrin H, Pillai K, Rodriguez E, Trochu F, Verheyden S, Wietgrefe M, Xiong W, Zaremba S, Ziegmann G (2014) Experimental determination of the permeability of engineering textiles: benchmark II. Compos A: Appl Sci Manuf 61:172–184CrossRefGoogle Scholar
  40. 40.
    Happel J (1959) Viscous flow relative to arrays of cylinders. AICHE J 5(2):174–177CrossRefGoogle Scholar
  41. 41.
    Bruschke MV, Advani SG (1993) Flow of generalized Newtonian fluids across a periodic array of cylinders. J Rheol 37(3):479–498CrossRefGoogle Scholar
  42. 42.
    Shimomukai K, Kanda H (2006) Numerical study of normal pressure distribution in entrance flow between parallel plates, I. Finite difference calculations. Electron Trans Numer Anal 23:202–218MathSciNetzbMATHGoogle Scholar
  43. 43.
    Subramanya K (1982) Flow in open channels, 3e. Vol. 1. Tata McGraw-Hill EducationGoogle Scholar
  44. 44.
    Hautier M, Lévêque D, Huchette C, Olivier P (2010) Investigation of composite repair method by liquid resin infiltration. Plast Rubber Compos 39(3–5):200–207CrossRefGoogle Scholar
  45. 45.
    Tabrizi SS (2012) Effect of mechanical abrasion on oil/water contact angle in metals. University of Wisconsin-Milwaukee, USAGoogle Scholar
  46. 46.
    Ferreira Luz F, Campus Amico S, de Lima Cunha A, Santos Barbosa E, Barbosa de Lima AG (2012) Applying computational analysis in studies of resin transfer moulding. Defect Diffus Forum 326–328 (2012) 158–163Google Scholar
  47. 47.
    Ferreira Luz F, de Lima Cunha A, Santos Barbosa E, Barbosa de Lima AG. Defect and Diffusion Forum 326–328 (2012) p 158–163Google Scholar

Copyright information

© Springer-Verlag France 2016

Authors and Affiliations

  • M.-Q. Thai
    • 1
    • 5
  • F. Schmidt
    • 2
  • G. Dusserre
    • 2
  • A. Cantarel
    • 3
  • L. Silva
    • 4
  1. 1.Faculty of Construction EngineeringUniversity of Transport and CommunicationsHanoiVietnam
  2. 2.Mines Albi, ICA (Institut Clément Ader)Université de ToulouseAlbi cedex 09France
  3. 3.IUT de Tarbes; ICA (Institut Clément Ader)Université de ToulouseTarbesFrance
  4. 4.Ecole centrale de Nantes, ICINantesFrance
  5. 5.Research & Application Center for Technology in Civil EngineeringUniversity of Transport and CommunicationsHanoiVietnam

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