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International Journal of Material Forming

, Volume 10, Issue 5, pp 653–669 | Cite as

Simulating squeeze flows in multiaxial laminates: towards fully 3D mixed formulations

  • Rubén Ibáñez
  • Emmanuelle Abisset-Chavanne
  • Francisco Chinesta
  • Antonio Huerta
Original Research

Abstract

Thermoplastic composites are widely considered in structural parts. In this paper attention is paid to squeeze flow of continuous fiber laminates. In the case of unidirectional prepregs, the ply constitutive equation is modeled as a transversally isotropic fluid, that must satisfy both the fiber inextensibility as well as the fluid incompressibility. When laminate is squeezed the flow kinematics exhibits a complex dependency along the laminate thickness requiring a detailed velocity description through the thickness. In a former work the solution making use of an in-plane-out-of-plane separated representation within the PGD – Poper Generalized Decomposition – framework was successfully accomplished when both kinematic constraints (inextensibility and incompressibility) were introduced using a penalty formulation for circumventing the LBB constraints. However, such a formulation makes difficult the calculation on fiber tractions and compression forces, the last required in rheological characterizations. In this paper the former penalty formulation is substituted by a mixed formulation that makes use of two Lagrange multipliers, while addressing the LBB stability conditions within the separated representation framework, questions never until now addressed.

Keywords

Squeeze flow Composite laminates Sheet forming Proper generalized decomposition Ericksen fluid Mixed formulation LBB condition 

Notes

Compliance with Ethical Standards

The authors declare that they have no conflict of interest.

References

  1. 1.
    Aghighi S, Ammar A, Metivier C, Normandin M, Chinesta F (2013) Non incremental transient solution of the Rayleigh-Bénard convection model using the PGD. J Non-Newtonian Fluid Mech 200:65–78CrossRefGoogle Scholar
  2. 2.
    Aghighi MS, Ammar A,Metivier C, Chinesta F (2015) Parametric solution of the Rayleigh-Bénard convection model by using the PGD: application to nanofluids. Int J Numer Methods Heat Fluid Flow 25(6):1252–1281Google Scholar
  3. 3.
    Ammar A, Mokdad B, Chinesta F, Keunings R (2006) A new family of solvers for some classes of multidimensional partial differential equations encountered in kinetic theory modeling of complex fluids. J Non-Newtonian Fluid Mech 139:153–176CrossRefzbMATHGoogle Scholar
  4. 4.
    Barnes JA, Cogswell FN (1989) Transverse flow processes in continuous fibre-reinforced thermoplastic composites. Composites 20/1:38–42CrossRefGoogle Scholar
  5. 5.
    Bersee HEN, Beukers A (2003) Consolidation of thermoplastic composites. J Thermoplast Compos Mater 16/5:433–455CrossRefGoogle Scholar
  6. 6.
    Bognet B, Leygue A, Chinesta F, Poitou A, Bordeu F (2012) Advanced simulation of models defined in plate geometries: 3D solutions with 2D computational complexity. Comput Methods Appl Mech Eng 201:1–12CrossRefzbMATHGoogle Scholar
  7. 7.
    Chinesta F, Ammar A, Leygue A, Keunings R (2011) An overview of the proper generalized decomposition with applications in computational rheology. J Non-Newtonian Fluid Mech 166:578–592CrossRefzbMATHGoogle Scholar
  8. 8.
    Chinesta F, Leygue A, Bognet B, Ghnatios C, Poulhaon F, Bordeu F, Barasinski A, Poitou A, Chatel S, Maison-Le-Poec S (2014) First steps towards an advanced simulation of composites manufacturing by automated tape placement. Int J Mater Form 7(1):81–92. http://www.springerlink.com/index/10.1007/s12289-012-1112-9
  9. 9.
    Ericksen JL (1959) Anisotropic fluids. Archive for rational mechanics and analysis, 231–237Google Scholar
  10. 10.
    Ghnatios C, Chinesta F, Binetruy C (2015) The squeeze flow of composite laminates. Int J Mater Form 8:73–83CrossRefGoogle Scholar
  11. 11.
    Ghnatios C, Abisset-Chavanne E, Binetruy C, Chinesta F, Advani S 3D modeling of squeeze flow of multiaxial laminates. J Non-Newtonian Fluid Mech. In Press. doi: 10.1016/j.jnnfm.2016.06.004
  12. 12.
    Goshawk JA, Navez VP, Jones RS (1997) Squeezing flow of continuous fibre-reinforced composites. J Non-Newtonian Fluid Mech 73/3:327–342CrossRefGoogle Scholar
  13. 13.
    Groves DJ, Bellamy AM, Stocks DM (1992) Anisotropic rheology of continuous fibre thermoplastic composites. Composites 23/2:75–80CrossRefGoogle Scholar
  14. 14.
    Gutowski TG, Cai Z, Bauer S, Boucher D, Kingery J, Wineman S (1987) Consolidation experiments for laminate composites. J Compos Mater 21/7:650–669CrossRefGoogle Scholar
  15. 15.
    Shuler SF, Advani SG (1996) Transverse squeeze flow of concentrated aligned fibers in viscous fluids. J Non-Newtonian Fluid Mech 65:47–74CrossRefGoogle Scholar
  16. 16.
    Shuler SF, Advani S (1997) Flow instabilities during the squeeze flow of multiaxial laminates. J Compos Mater 31/21:2156–2160Google Scholar
  17. 17.
    Spencer AJM (2000) Theory of fabric-reinforced viscous fluids. Compos Part A 31:1311–1321CrossRefGoogle Scholar

Copyright information

© Springer-Verlag France 2016

Authors and Affiliations

  • Rubén Ibáñez
    • 1
  • Emmanuelle Abisset-Chavanne
    • 1
  • Francisco Chinesta
    • 1
  • Antonio Huerta
    • 2
  1. 1.ESI GROUP Chair, ICI - High Performance Computing Institute, Ecole Centrale de NantesNantesFrance
  2. 2.Laboratori de Càlcul NumèricUniversitat Politècnica de CatalunyaBarcelonaSpain

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