Remeshing procedure for discrete membrane finite element: application to woven composite forming

Authors

  • Abel Cherouata Charles Delaunay Institute, Equipe Gamma3, University of Technology of Troyes, 12 rue Marie Curie, BP2060, 10010 Troyes, Cedex, France
  • Laurence Moreau Charles Delaunay Institute, Equipe Gamma3, University of Technology of Troyes, 12 rue Marie Curie, BP2060, 10010 Troyes, Cedex, France
  • Rezak Ayad Laboratoire d’Ingénierie et de Sciences des Matériaux/LISM, Université de Reims Champagne-Ardenne, UFR SEN, Moulin de la Housse, BP 1039, 51687 Reims, Cedex 2, France
  • Tarak Ben Zineb Université de Lorraine/LEMTA, 2 rue Jean Lamour, 54500 Vandoeuvre-les-Nancy, France

DOI:

https://doi.org/10.13052/17797179.2012.702427

Keywords:

pre-impregnated fabric, FEM, adaptive remeshing, composite forming, FRQ element, truss element

Abstract

Pre-impregnated woven fabric is an increasingly important component as the reinforcement phase of composite materials for many mechanical structures (automotive and aerospace). Modelling woven fabrics is difficult due, in particular, to the need to simulate the response both at the scale of the entire fabric and at the meso-level, the scale of the fibre that composes the weave. Here, we present new finite element for the simulation of the 3D, preimpregnated woven fabric preform. Continuum-level modelling technique that, through the use of an appropriate bi-component unit cell (fiber rotation quadrilateral element connected to truss elements), captures the deformation of the mesostructure of the fabric without explicitly modelling every fibre. Simulations of the experiments demonstrate that the finite elements are capable of efficiently simulating large, complex structures and forming processes.

Downloads

Download data is not yet available.

References

Abaqus theory. (2009). User's Manual. Karlsson & Sorensen, Inc. Hibbitt.

Allman, D.J. (1984). A compatible triangular element including vertex rotations for plane elasticity.

Computers & Structures, 19, 1–8.

Ayad, R. (1993). Eléments finis de plaque et coque en formulation mixte avec projection en cisaillement.

Thèse de Doctorat, UTC, Mars.

Ayad, R., Rigolot, A., & Talbi, N. (2001). An improved three-node hybrid-mixed element for Mindlin

Reissner plates. International Journal for Numerical Methods in Engineering, 51, 919–942.

Babuska, I., Zienkiewicz, O.C., Gago, J., & Olivera D.A. (Eds.). (1986). Accuracy estimates and adaptive

refinements in finite element computations. New York: Wiley.

Baker, T.J. (1989). Automatic mesh generation for complex three-dimensional regions using a constrained

Delaunay triangulation. Engineering with Computers, 5, 161–175.

Bergan, P.G., & Felippa, C.A. (1985). A triangular membrane element with rotational degrees of freedom.

Computer Methods in Applied Mechanics and Engineering, 50, 25–69.

Bergsma, O.K., & Huisman, J. (1988). Deep drawing of fabric reinforced thermoplastic. In C.A. Brebbia,

W.P. de Wilde and W.R. Blain (Eds.), 2nd international conference of Computer Aided Design

in Composite Material Technology, Southampton, (pp. 323–333). Berlin: Springer-Verlag.

Boisse, P., Buet, K., Gasser, A., & Launay, J. (2001). Meso/macro-mechanical behaviour of textile reinforcements

for thin composites. Composites Science and Technology, 61(3), 395–401.

Boisse, P., Gasser, A., Hagege, B., & Billoet, J.L. (2005). Analysis of the mechanical behaviour of

woven fibrous material using virtual tests at the unit cell level. International Journal of Materials

Sciences, 40, 5955–5962.

Borouchaki, H., & Cherouat, A. (2003). Drapage géométrique des composites. Comptes rendus de

l’Académie des Sciences Paris, Serie II B, Mecanique des Solides et des Structures, 331, 437–442.

Borouchaki, H., Cherouat, A., & Billoët, J.L. (1999). GeomDrap new computer aided design and manufacturing

for advanced textile composites, Version 1. Troyes, France: UTT Internal Report.

Borouchaki, H., Cherouat, A., Laug, P., & Saanouni, K. (2002). Adaptative meshing for ductile fracture

prediction in metal forming. Comptes Rendus Mecanique, 330(10), 709–716.

Cherouat, A., & Billoët, J.L. (2001). Mechanical and numerical modelling of composite manufacturing

processes deep-drawing and laying-up of thin pre-impregnated woven fabrics. Journal of Materials

Processing Technology, 118, 460–471.

Cherouat, A., & Borouchaki, H. (2009). Present state of the art of composite fabric forming: geometrical

and mechanical approaches. Materials, 2(4), 1835–1857.

Cherouat, A., Borouchaki, H., & Giraud-Moreau, L. (2010). Mechanical and geometrical approaches

applied to composite fabric forming. International Journal of Material Forming. doi: 10.1007/

s12289-010-0692-5

Cherouat, A., Gelin, J.C., Boisse, P., & Sabhi, H. (1995). Numerical modeling of glass woven fabric deepdrawing

using finite element method. European Journal of Computational Mechanics, 4, 159–182.

Cherouat, A., Borouchaki, H., & Billoët, J.L. (2005). Geometrical and mechanical draping of composite

fabric. European Journal of Computational Mechanics, 14(6–7), 693–708.

Cho, J.-W., & Yang, D.-Y. (2002). A mesh refinement scheme for sheet metal forming analysis. In Proceedings

of the 5th International Conference, NUMISHEET’02 (pp. 307–312).

Dafalias, Y.F. (1983). Corotational rates for kinematic hardening at large plastic deformations. Journal

of Applied Mechanics, 50, 561–565.

Duhovic, M., & Bhattacharyya, D. (2006). Simulating the deformation mechanisms of knitted fabric

composites. Composites Part A: Applied Science and Manufacturing, 37(11), 1897–1915.

ElHami, A., Radi, B., & Cherouat, A. (2009). Treatment of the composite fabric’s shaping using a

Lagrangian formulation. Mathematical and Computer Modelling, 49(7–8), 1337–1349.

Parsons, E.M., Weerasooriya, T., Sarva, S., & Socrate, S. (2010). Impact of woven fabric: Experiments

and mesostructure-based continuum-level simulations. Journal of the Mechanics and Physics of Solids,

, 1995–2021.

Fan, J.P., Tang, C.Y., Tsui, C.P., Chan, L.C., & Lee, T.C. (2006). 3D finite element simulation of deep

drawing with damage development. International Journal of Machine Tools and Manufacture, 46

(9), 1035–1044.

Fourment, L., & Chenot, J.L. (1994). Adaptive remeshing and error control for forming processes.

Revue européenne des éléments finis, 3(2), 247–279.

Gifford, L.N. (1979). More on distorted isoparametric elements. International Journal for Numerical

Methods in Engineering, 14, 290–291.

Gilormini, P., & Roudier, P. (1993). Abaqus and Finite Strain, Rapport interne n° 140. Cahchan, France.

Giraud-Moreau, L., Borouchaki, H., & Cherouat, A. (2005). Remaillage adaptatif pour la mise en forme

des tôles minces. Comptes rendus de l’Académie des Sciences Paris, Serie II B, Mécanique des

Solides et des Structures, 333(4), 371–378.

Gommers, B., Verpoest, I., & Van Houtte, P. (1996). Modelling the elastic properties of knitted fabricreinforced

composites. Composites science and technology, 56, 685–694.

Hagège, B., Boisse, P., & Billoët, J.-L. (2005). Finite element analyses of knitted composite reinforcement

at large strain. European Journal of Computational Mechanics, 14(6–7), 767–776.

Hancock, S.G., & Potter, K.D. (2005). Inverse drape modelling – an investigation of the set of shapes

that can be formed from continuous aligned woven fibre reinforcements. Composites Part A:

Applied Science and Manufacturing, 36(7), 947–953.

Harrison, P., Clifford, M.J., Long, A.C., & Rudd, C.D. (2004). A constituent-based predictive approach

to modelling the rheology of viscous textile. Composites Part A: Applied Science and Manufacturing,

, 915–931.

Hou, M., Ye, L., & Mai, Y.W. (1997). Manufacturing process and mechanical properties of thermoplastic

composite components. Journal of Materials Processing Technology, 63, 334–338.

Lim, T.C., Ramakrishna, S., & Shang, H.M. (1999). Optimization of the formability of knitted fabric

composite sheet by means of combined deep drawing and stretch forming. Journal of Materials Processing

Technology, 89–90, 99–103.

Liu, L., Chen, J., Li, X., & Sherwood, J. (2005). Two-dimensional macro-mechanics shear models of

woven fabrics. Composites Part A: Applied Science and Manufacturing, 36, 105–114.

Lomov, S.V., Ivanov, D.S., Verpoest, I., Zako, M., Kurashiki, T., Nakai, H., & Hirosawa, S. (2007).

Meso-FE modelling of textile composites: Road map, data flow and algorithms. Composites Science

and Technology, 67, 1870–1891.

Long, A.C. (2001). Process modelling for liquid moulding of braided performs. Composites Part A:

Applied Science and Manufacturing, 32(7), 941–953.

Long, A.C., & Rudd, C.D. (1994). A simulation of reinforcement deformation during the production of

preform for liquid moulding processes. Proceedings of the Institution of Mechanical Engineers –

Part B: Management and Engineering Manufacture, 208, 269–278.

Luo, Y., & Verpoest, I. (2002). Biaxial tension and ultimate deformation of knitted fabric reinforcements.

Composites Part A: Applied Science and Manufacturing, 33, 197–203.

Mark, C., & Taylor, H.M. (1956). The fitting of woven cloth to surfaces. Journal of the Textile Institute,

, 477–488.

Oden, J.T., Demkowicz, L., Rachowicz, W., & Westermann, T.A. (1989). Towards a universal h-p

adaptive finite element strategy, part 2. A posteriori error estimation. Computer Methods in

Applied Mechanics and Engineering, 77, 113–180.

Padmanabhan, K.A. (2008). Metal forming at very low strain rates. In Encyclopedia of Materials. Science

and Technology (pp. 5384–5389). UK: Elsevier Science.

Peng, X., & Cao, J. (2002). A dual homogenization and finite element approach for material characterization

of textile composites. Composites Part B: Engineering, 33, 45–56.

Peng, X., & Cao, J. (2005). A continuum mechanics-based nonorthogonal constitutive model for woven

composite fabrics. Composites Part A: Applied Science and Manufacturing, 36, 859–874.

Pickett, A.K., Creech, G., & de Luca, P. (2005). Simplified and advanced simulation methods for prediction

of fabric draping. European Journal of Computational Mechanics, 14(6–7), 677–691.

Potluri, P., Sharma, S., & Ramgulam, R. (2001). Comprehensive drape modelling for moulding 3D

textile preforms. Composites Part A: Applied Science and Manufacturing, 32(10), 1415–1424.

Potluri, P., Parlak, I., Ramgulam, R., & Sagar, T.V. (2006). Analysis of tow deformations in textile

preforms subjected to forming forces. Composites Science and Technology, 66(2), 297–305.

Rozant, O., Bourban, P.E., & Manson, J.A.E. (2000). Drapability of dry textile fabrics for stampable

thermoplastic performs. Composites Part A: Applied Science and Manufacturing, 31, 1167–1177.

Rudd, C.D., & Long, A.C. 1997. Liguid molding technologies. Cambridge: Woodhead Publishing.

Sharma, S.B., & Sutcliffe, M.P.F. (2004). A simplified finite element model for draping of woven material.

Composites Part A: Applied Science and Manufacturing, 35, 637–643.

Spencer, A.J.M. (2000). Theory of fabric-reinforced viscous fluid. Composites Part A: Applied Science

and Manufacturing, 31, 1311–1321.

Lim, T.-C., & Ramakrishna, S. (2002). Modelling of composite sheet forming: A review. Composites

Part A: Applied science and manufacturing, 33, 515–537.

Ten Thije, R.H.W., Akkerman, R., & Huetink, J. (2007). Large deformation simulation of anisotropic

material using an updated Langrangian finite element method. Computer Methods in Applied

Mechanics and Engineering, 196(33–34), 3141–3150.

Trochu, F., Ruiz, E., Achim, V., & Soukane, S. (2006). Advanced numerical simulation of liquid composite

molding for process analysis and optimization. Composites Part A: Applied Science and Manufacturing,

, 890–902.

Umer, R., Bickerton, S., & Fernyhough, A. (2008). Modelling the application of wood fibre reinforcements

within liquid composite moulding processes. Composites Part A: Applied Science and

Manufacturing, 39(4), 624–639.

Van Der Ween, F. (1991). Algorithms for draping fabrics on doubly curved surfaces. International Journal

for Numerical Methods in Engineering, 31, 1414–1426.

Vanclooster, K., Lomov, S.V., & Verpoest, I. (2009). Experimental validation of forming simulations of

fabric reinforced polymers using an unsymmetrical mould configuration. Composites Part A: Applied

Science and Manufacturing, 40(4), 530–539.

Vilnis Frishfelds, F., Staffan Lundström, T., & Jakovics, A. (2008). Bubble motion through non-crimp

fabrics during composites manufacturing. Composites Part A: Applied Science and Manufacturing,

(2), 243–251.

Warby, M.K., Whiteman, J.R., Jiang, W.-G., Warwick, P., & Wright, T. (2003). Finite element simulation

of thermoforming processes for polymer sheets. Mathematics and Computers in Simulation, 61,

–218.

Xue, P., Peng, X., & Cao, J. (2003). A non-orthogonal constitutive model for characterizing woven composites.

Composites Part A: Applied Science and Manufacturing, 34, 183–193.

Yu, W.R., Pourboghrat, F., Chung, K., Zamploni, M., & Kang, T.J. (2002). Non-orthogonal constitutive

equation for woven fabric reinforced thermoplastic composites. Composites Part A: Applied Science

and Manufacturing, 33, 1095–1105.

Zhu, Y.Y., Zacharia, T., & Cescotto, S. (1997). Application of fully automatic remeshing to complex

metal forming analyses. Computers & Structures, 62(3), 417–427.

Zienkiewicz, O.C., & Zhu, J.Z. (1987). A simple error estimator and adaptive procedure for practical

engineering analysis. International Journal for Numerical Methods in Engineering, 24, 337–357

Downloads

Published

2012-02-07

How to Cite

Cherouata, A., Moreau, L., Ayad, R., & Zineb, T. B. (2012). Remeshing procedure for discrete membrane finite element: application to woven composite forming. European Journal of Computational Mechanics, 21(1-2), 4–21. https://doi.org/10.13052/17797179.2012.702427

Issue

Section

Original Article

Most read articles by the same author(s)