Top

International Journal of Material Forming

Published in:

02-07-2016 | Original Research

BEM computation of 3D Stokes flow including moving front

Authors: M.-Q. Thai, F. Schmidt, G. Dusserre, A. Cantarel, L. Silva

Published in: International Journal of Material Forming | Issue 4/2017

Activate our intelligent search to find suitable subject content or patents.

search-config

AI-assisted search

Off

Abstract

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.

previous article Evaluation of the shear stresses on surface structured workpieces in dry forming using a novel pin-on-cylinder tribometer with axial feed

next article Improvement strategy for edge waviness in roll bending process of corrugated sheet metals

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

über 102.000 Bücher
über 537 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Finance + Banking
Management + Führung
Marketing + Vertrieb
Maschinenbau + Werkstoffe
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 390 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Maschinenbau + Werkstoffe

Jetzt Wissensvorsprung sichern!

inform now

Beukers A (2001) Polymer matrix composites : applications. Encyclopedia of Materials : Science and Technology. Elsevier, Oxford. p 7384–7388

Jones RM (1998) Mechanics of composite materials. CRC Press

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 Toulouse

Patel N, Lee LJ (1995) Effects of fiber mat architecture on void formation and removal in liquid composite molding. Polym Compos 16(5):386–399CrossRef

Rouison D, Sain M, Couturier M (2004) Resin transfer molding of natural fiber reinforced composites: cure simulation. Compos Sci Technol 64(5):629–644CrossRef

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):635–638CrossRef

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):619–622

Chen X, Papathanasiou TD (2007) Micro-scale modeling of axial flow through unidirectional disordered fiber arrays. Compos Sci Technol 67:1286–1293CrossRef

Brebbia CA, Dominguez J (1992) Boundary elements: an introductory course. Computational Mechanics Publications, 2nd edition

10.

Paris F, Canas J (1997) Boundary element method : fundamentals and applications. Oxford University Press

11.

Osher S, Sethian JA (1988) Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations. J Comput Phys 79(1):12–49MathSciNetCrossRefMATH

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 édition

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):236–250CrossRef

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. 554–557:447–455

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):890–902CrossRef

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. 1385–1419

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):277–302MathSciNetCrossRefMATH

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):1235–1244CrossRef

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):1067–1080CrossRef

20.

Gebart BR (1992) Permeability of unidirectional reinforcements for RTM. J Compos Mater 26:1100–1133CrossRef

21.

Berdichevsky AL, Cai Z (1993) Preform permeability predictions by self-consistent method and finite element simulation. Polym Compos 14(2):132–143CrossRef

22.

Dusserre G, Jourdain E, Bernhart G. Effect of deformation on knitted glass preform in-plane permeability. Polym Compos 32(1): 18–28

23.

Sharma S (2010) On the improvement of permeability assessment of fibrous materials. In MS Aerospace engineering. Wichita State University

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):612–619CrossRef

25.

Shirley P, Tuchman A (1990) A polygonal approximation to direct scalar volume rendering. SIGGRAPH Comput Graph 24(5):63–70CrossRef

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):626–650MathSciNetCrossRefMATH

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 23–32CrossRef

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):37–61CrossRefMATH

29.

Nerantzaki MS, Kandilas CB (2008) A boundary element method solution for anisotropic nonhomogeneous elasticity. Acta Mech 200(3):199–211CrossRefMATH

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): 1235–1244

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):725–732CrossRef

32.

Hunter P, Pullan A (2003) FEM/BEM notes. Department of Engineering Science. University of Auckland, New Zealand

33.

Fratantonio M, Rencis JJ (2000) Exact boundary element integrations for two-dimensional Laplace equation. Eng Anal Bound Elem 24(4):325–342CrossRefMATH

34.

Telles FJC, Oliveira FR (1994) Third degree polynomial transformation for boundary element integrals: further improvements. Elsevier, Kidlington, Royaume-Uni

35.

Newman TS, Yi H (2006) A survey of the marching cubes algorithm. Comput Graph 30(5):854–879CrossRef

36.

Oh S, Koo BK (2007) Data perturbation for fewer triangles in marching tetrahedra. Graph Model 69(3):211–218CrossRef

37.

Sharma S, Siginer DA (2010) Permeability measurement methods in porous media of fiber reinforced composites. Appl Mech Rev 63(2):020802CrossRef

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):1157–1168CrossRef

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 61:172–184CrossRef

40.

Happel J (1959) Viscous flow relative to arrays of cylinders. AICHE J 5(2):174–177CrossRef

41.

Bruschke MV, Advani SG (1993) Flow of generalized Newtonian fluids across a periodic array of cylinders. J Rheol 37(3):479–498CrossRef

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 23:202–218MathSciNetMATH

43.

Subramanya K (1982) Flow in open channels, 3e. Vol. 1. Tata McGraw-Hill Education

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):200–207CrossRef

45.

Tabrizi SS (2012) Effect of mechanical abrasion on oil/water contact angle in metals. University of Wisconsin-Milwaukee, USA

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) 158–163

47.

Ferreira Luz F, de Lima Cunha A, Santos Barbosa E, Barbosa de Lima AG. Defect and Diffusion Forum 326–328 (2012) p 158–163

Title: BEM computation of 3D Stokes flow including moving front
Authors: M.-Q. Thai
F. Schmidt
G. Dusserre
A. Cantarel
L. Silva
Publication date: 02-07-2016
Publisher: Springer Paris
Published in: International Journal of Material Forming / Issue 4/2017
Print ISSN: 1960-6206
Electronic ISSN: 1960-6214
DOI: https://doi.org/10.1007/s12289-016-1302-y

Springer Professional

Abstract

Please log in to get access to your license.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Springer Professional "Technik"

Other articles of this Issue 4/2017

Erichsen cupping test on thermosetting CFRP sheets

Numerical implementation of an elastic-viscoplastic constitutive model to simulate the mechanical behaviour of amorphous polymers

Assessment of anisotropic hardening models for conventional deep drawing processes

Application of the Kalai-Smorodinsky approach in multi-objective optimization of metal forming processes

Evaluation of the shear stresses on surface structured workpieces in dry forming using a novel pin-on-cylinder tribometer with axial feed

Experimental prediction of sheet metal formability of AW-5754 for non-linear strain paths by using a cruciform specimen and a blank holder with adjustable draw beads on a sheet metal testing machine

Premium Partners