International Journal of Material Forming

, Volume 12, Issue 2, pp 295–306 | Cite as

A simple microstructural viscoelastic model for flowing foams

  • Rubén Ibáñez
  • Adrien Scheuer
  • Emmanuelle Abisset-Chavanne
  • Francisco ChinestaEmail author
  • Antonio Huerta
  • Roland Keunings
Original Research


The numerical modelling of forming processes involving the flow of foams requires taking into account the different problem scales. Thus, in industrial applications a macroscopic approach is suitable, whereas the macroscopic flow parameters depend on the cellular structure: cell size, shape, orientation, etc. Moreover, the shape and orientation of the cells are induced by the flow. A fully microscopic description remains useful to understand the foam behaviour and the topological changes induced by the cell elongation or distortion, however, from an industrial point of view, microscopic simulations remain challenging to address practical applications involving flows in complex 3D geometries. In this paper, we propose a viscoelastic flow model where the foam microstructure is represented from suitable microstructure descriptors whose evolution is governed by the macroscopic flow kinematics.


Flowing foams Viscoelasticity Conformation Microstructural description 



This project has received funding from the European Unions Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement No. 675919.

Compliance with Ethical Standards

Conflict of interests

The authors declare that they have no conflict of interest.


  1. 1.
    Benito S, Bruneau C-H, Colin T, Gay C, Molino F (2008) An elasto-visco-plastic model for immortal foams or emulsions. Eur Phys J E 25:225–251CrossRefGoogle Scholar
  2. 2.
    Bikard J, Bruchon J, Coupez T, Vergnes B (2005) Numerical prediction of the foam structure of polymeric materials by direct 3D simulation of their expansion by chemical reaction based on a multidomain method. J Mater Sci 40/22:5875–5881CrossRefGoogle Scholar
  3. 3.
    Binetruy C, Chinesta F, Keunings R (2015) F Flows in Polymers, Reinforced Polymers and Composites. A multiscale approach. Springer, SpringerbriefsGoogle Scholar
  4. 4.
    Cheddadi I, Saramito P, Raufaste C, Marmottant P, Graner F (2008) Numerical modelling of foam Couette flows. Eur Phys J E 27(/2):123–133CrossRefGoogle Scholar
  5. 5.
    Chinesta F (2013) From single-scale to two-scales kinetic theory descriptions of rods suspensions. Arch Comput Meth Eng 20/1:1–29MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Cohen-Addad S, Hohler R, Pitois O (2013) Flow in foams and flowing foams. Annu Rev Fluid Mech 45:241–267MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Feyel F (2003) A multilevel finite element method (FE2) To describe the response of highly non-linear structures using generalized continua. Comput Methods Appl Mech Eng 192/28:3233–3244CrossRefzbMATHGoogle Scholar
  8. 8.
    Halin P, Lielens G, Keunings R, Legat V (1998) The Lagrangian particle method for macroscopic and micro-macro viscoelastic flow computations. J Non-Newtonian Fluid Mech 79:387–403CrossRefzbMATHGoogle Scholar
  9. 9.
    Jeffery GB (1922) The motion of ellipsoidal particles immersed in a viscous fluid. Proc R Soc London A102:161–179CrossRefzbMATHGoogle Scholar
  10. 10.
    Karimi M, Droghetti H, Marchisio DL (2017) PUFOam: a novel open-source CFD solver for the simulation of polyurethane foams. Comput Phys Commun 217:138–148CrossRefGoogle Scholar
  11. 11.
    Keunings R (2004) Micro-macro methods for the multiscale simulation viscoelastic flow using molecular models of kinetic theory. In: Binding DM, Walters K (eds) Rheology reviews. British Society of Rheology, Aberystwyth, pp 67–98Google Scholar
  12. 12.
    Lamari H, Ammar A, Cartraud P, Legrain G, Jacquemin F, Chinesta F (2010) Routes for efficient computational homogenization of nonlinear materials using the Proper Generalized Decomposition. Arch Comput Meth Eng 17/4:373–391MathSciNetCrossRefzbMATHGoogle Scholar
  13. 13.
    Tlili S, Gay C, Graner F, Marcq P, Molino F, Saramito P (2015) Mechanical formalisms for tissue dynamics. Eur Phys J E 38:33–63CrossRefGoogle Scholar

Copyright information

© Springer-Verlag France SAS, part of Springer Nature 2018

Authors and Affiliations

  • Rubén Ibáñez
    • 1
  • Adrien Scheuer
    • 1
    • 4
  • Emmanuelle Abisset-Chavanne
    • 1
  • Francisco Chinesta
    • 2
    Email author
  • Antonio Huerta
    • 3
  • Roland Keunings
    • 4
  1. 1.ICI - High Performance Computing Institute at Ecole Centrale de NantesESI GROUP Chair on Advanced Modeling and Simulation of Manufacturing ProcessesNantesFrance
  2. 2.PIMM, ENSAM ParisTech, ESI GROUP Chair on Advanced Modeling and Simulation of Manufacturing ProcessesParisFrance
  3. 3.Laboratori de Càlcul NumèricUniversitat Politècnica de Catalunya, BarcelonaTechBarcelonaSpain
  4. 4.ICTEAMUniversité catholique de LouvainLouvain-la-NeuveBelgium

Personalised recommendations