A generalised method for the coupling of a parallelogram-like unit cell with a macroscopic finite element to simulate the behaviour of textiles


To simulate the behaviour of textiles, three major characteristics are important, kinematic fibre interaction, shear behaviour, and thickness changes of the fabric caused by shearing. Instead of anisotropic continuum mechanical models normally used, a macroscopic finite element coupled with an internal unit cell, made of beam elements is proposed here. The beam elements represent the yarns. The method is generalized for unit cells with parallelogram shaped unit cell geometries. The coupled unit cell model can improve finite element simulations, in terms of calculation time and modelling effort, because the major characteristics named before can be described in detail by the unit cell without using full-scale models.

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  1. 1.

    Kawabata S, Niwa M, Kawai H (1973) The finite-deformation theory of plain-weave fabrics part 1–3. J Text Inst 64(1):21–46

    Article  Google Scholar 

  2. 2.

    Boisse P, Borr M, Buet K, Cherouat A (1997) Finite element simulations of textile composite forming including the biaxial fabric behaviour. Compos Part B 28(4):453–464

    Article  Google Scholar 

  3. 3.

    Boisse P, Gasser A, Hivet G (2001) Analyses of fabric tensile behaviour determination of the biaxial tension-strain surfaces and their use in forming simulations. Compos A: Appl Sci Manuf 32(10):1395–1414

    Article  Google Scholar 

  4. 4.

    Haug E, De Kermel P, Gawenat B, Michalski A (2007) Industrial design and analysis of structural membranes. In: International conference on textile composites and inflatable structures STRUCTURAL MEMBRANES, Barcelona, Spain

  5. 5.

    Feyel F (1999) Multiscale FE2 elastoviscoplastic analysis of composite structures. Comput Mater Sci 16(1):344–354

    Article  Google Scholar 

  6. 6.

    Feyel F, Chaboche JL (2000) FE2 multiscale approach for modelling the elastoviscoplastic behaviour of long fibre sic/ti composite materials. Comput Methods Appl Mech Eng 183(3–4):309–330

    Article  Google Scholar 

  7. 7.

    Feyel F (2003) A multilevel finite element method \(\left (\text {FE}^{2}\right )\) to describe the response of highly non-linear structures using generalized continua. Comput Methods Appl Mech Eng 192(28):3233–3244

    Article  Google Scholar 

  8. 8.

    Pickett AK, Queckbörner T, De Luca P, Haug E (1995) An explicit finite element solution for the forming prediction of continuous fibre-reinforced thermoplastic sheets. Composites Manufacturing 6(3–4):237–243. 3rd international conference on flow processes in composite materials 94

    Article  Google Scholar 

  9. 9.

    de Luca P, Lefébure P, Pickett AK (1998) Selected papers presented at the fourth international conference on flow processes in composite material. Compos A: Appl Sci Manuf 29(1–2):101–110

    Article  Google Scholar 

  10. 10.

    Pickett AK (2002) Review of finite and element simulation and methods and applied to manufacturing and failure prediction and in and composites structures. Appl Compos Mater 9:43–58

    Article  Google Scholar 

  11. 11.

    Grujicic M, Bell WC, He T, Cheeseman BA (2008) Development and verification of a meso-scale based dynamic material model for plain-woven single-ply ballistic fabric. J Mater Sci 43(18):6301–6323

    Article  Google Scholar 

  12. 12.

    Gatouillat S, Bareggi A, Vidal-Sallé E, Boisse P (2013) Meso modelling for composite preform shaping - simulation of the loss of cohesion of the woven fibre network. Compos A: Appl Sci Manuf 54:135–144

    Article  Google Scholar 

  13. 13.

    Lomov SV, Ivanov DS, Verpoest I, Zako M, Kurashiki T, Nakai H, Hirosawa S (2007) Meso-fe modelling of textile composites: road map, data flow and algorithms. Combust Sci Technol 67(9):1870–1891

    Article  Google Scholar 

  14. 14.

    Kaiser B, Masseria F, Berger A, Hühn D (2014) Manufacturing process simulation of fiber reinforced composites – industrial software tools and state of the art in research. In: NAFEMS seminar: simulation of composites – a closed process chain?. October 28 - 29, 2014, Leipzig, Germany

  15. 15.

    (2015) http://www.wovencomposites.org. Woven composites benchmark forum

  16. 16.

    Khan MA, Mabrouki T, Vidal-Sallé EE, Boisse P (2010) Numerical and experimental analyses of woven composite reinforcement forming using a hypoelastic behaviour. Application to the double dome benchmark. J Mater Process Technol 210(2):378–388

    Article  Google Scholar 

  17. 17.

    Komeili M, Milani AS (2016) On effect of shear-tension coupling in forming simulation of woven fabric reinforcements. Compos Part B 99:17–29

    Article  Google Scholar 

  18. 18.

    Allaoui S, Boisse P, Chatel S, Hamila N, Hivet G, Soulat D, Vidal-Sallé E (2011) Experimental and numerical analyses of textile reinforcement forming of a tetrahedral shape. Compos A: Appl Sci Manuf 42 (6):612–622

    Article  Google Scholar 

  19. 19.

    Hivet G, Allaoui S, Cellard C (2015) Effect of inter-ply sliding on the quality of multilayer interlock dry fabric preforms. Compos A: Appl Sci Manuf 68:336–345

    Google Scholar 

  20. 20.

    Yin H, Peng X, Tongliang D, Guo Z (2014) Draping of plain woven carbon fabrics over a double-curvature mold. Compos Sci Technol 92(0):64–69

    Article  Google Scholar 

  21. 21.

    Gereke T, Döbrich O, Hübner M, Cherif C (2013) Experimental and computational composite textile reinforcement forming: a review. Compos A: Appl Sci Manuf 46(0):1–10

    Article  Google Scholar 

  22. 22.

    Carvelli V, Poggi C (2001) A homogenization procedure for the numerical analysis of woven fabric composites. Compos A: Appl Sci Manuf 32(10):1425–1432

    Article  Google Scholar 

  23. 23.

    Otero F, Oller S, Martinez X, Salom0́n O (2015) Numerical homogenization for composite materials analysis. Comparison with other micro mechanical formulations. Compos Struct 122:405–416

    Article  Google Scholar 

  24. 24.

    Jacques S, De Baere I, Van Paepegem W (2014) Application of periodic boundary conditions on multiple part finite element meshes for the meso-scale homogenization of textile fabric composites. Compos Sci Technol 92:41–54

    Article  Google Scholar 

  25. 25.

    Parisch H (2003) Festkorper-Kontinuumsmechanik̈ Vieweg Teubner

  26. 26.

    Newton I, Motte A, Machin J (1729) The mathematical principles of natural philosophy. B Motte

  27. 27.

    Sanchez-Palencia E, Zaoui AC (1987) Homogenization techniques for composite media lecture notes in physics. Springer, Berlin

    Google Scholar 

  28. 28.

    Surana KS, Sorem RM (1989) Geometrically non-linear formulation for three dimensional curved beam elements with large rotations. Int J Numer Methods Eng 28(1):43–73

    Article  Google Scholar 

  29. 29.

    Surana KS (1983) Geometrically non-linear formulation for two dimensional curved beam elements. Comput Struct 17(1):105–114

    Article  Google Scholar 

  30. 30.

    Surana KS (1982) Geometrically nonlinear formulation for the axisymmetric shell elements. Int J Numer Methods Eng 18(4):477–502

    MathSciNet  Article  Google Scholar 

  31. 31.

    Cao J, Akkerman R, Boisse P, Chen J, Cheng HS, de Graaf EF, Gorczyca JL, Harrison P, Hivet G, Launay J, Lee W, Liu L, Lomov SV, Long A, de Luycker E, Morestin F, Padvoiskis J, Peng X, Sherwood J, Stoilova TZ, Tao XM, Verpoest I, Willems A, Wiggers J, Yu TX, Zhu B (2008) Characterization of mechanical behavior of woven fabrics experimental methods and benchmark results. Compos A: Appl Sci Manuf 39(6):1037–1053

    Article  Google Scholar 

  32. 32.

    Stoilova T, Lomov S (2004) Round – robin formability study characterisation of glass/polypropylene fabrics. http://www.wovencomposites.org

  33. 33.

    Harrison P, Clifford MJ, Long AC (2004) Shear characterisation of viscous woven textile composites: a comparison between picture frame and bias extension experiments. Combust Sci Technol 64:1453–1465

    Article  Google Scholar 

  34. 34.

    Peng X, Rehman ZU (2011) Textile composite double dome stamping simulation using a non-orthogonal constitutive model. Compos Sci Technol 71(8):1075–1081

    Article  Google Scholar 

  35. 35.

    Peng X, Guo Z, Du T, Yu W-R (2013) A simple anisotropic hyperelastic constitutive model for textile fabrics with application to forming simulation. Compos Part B 52:275–281

    Article  Google Scholar 

  36. 36.

    Group ESI (2013) 100-102 Avenue de Suffren 75015 Paris FR. PAM-Crash Solver Reference Manual, edition

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Correspondence to Benjamin Kaiser.

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This study was sponsored by ESI Group, 100-102 Avenue de Suffren, 75015 Paris, FRANCE. The authors declare that they have no conflict of interest.

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Kaiser, B., Pyttel, T. & Duddeck, F. A generalised method for the coupling of a parallelogram-like unit cell with a macroscopic finite element to simulate the behaviour of textiles. Int J Mater Form 13, 103–116 (2020). https://doi.org/10.1007/s12289-019-01472-9

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  • Textile composites
  • Woven fabrics
  • Draping simulation
  • Fibre interaction
  • Non-orthogonal unit cells
  • Beam based unit cells
  • Coupled multi-scale models
  • F E 2