Computational Particle Mechanics

, Volume 4, Issue 1, pp 3–12 | Cite as

An axisymmetric PFEM formulation for bottle forming simulation

  • Pavel B. Ryzhakov


A numerical model for bottle forming simulation is proposed. It is based upon the Particle Finite Element Method (PFEM) and is developed for the simulation of bottles characterized by rotational symmetry. The PFEM strategy is adapted to suit the problem of interest. Axisymmetric version of the formulation is developed and a modified contact algorithm is applied. This results in a method characterized by excellent computational efficiency and volume conservation characteristics. The model is validated. An example modelling the final blow process is solved. Bottle wall thickness is estimated and the mass conservation of the method is analysed.


Glass manufacturing Numerical modelling Lagrangian Axisymmetric Final blow 



The author expresses his gratitude to the Spanish Ministerio de Economia y Competitividad for the FPDI-2013-18471 grant that allowed to perform this work.


  1. 1.
    Pfaender HG (2012) Schott guide to glass. Springer Science and Business Media, BerlinGoogle Scholar
  2. 2.
    Miller GL, Sullivan C (1984) Machine-made glass containers and the end of production for mouth-blown bottles. Hist Archaeol 18/2:83–96Google Scholar
  3. 3.
    Lerman R (2016) eBottles a history of glass bottle and glass jar manufacturing. Accessed 16 Mar 2016
  4. 4.
    Cesar de Sa JMA (1986) Numerical modelling of glass forming processes. Eng Comput 3:266–275CrossRefGoogle Scholar
  5. 5.
    Matthew H (2002) Numerical simulation of glass forming and conditioning. J Am Ceram Soc 85(5):1047–1056Google Scholar
  6. 6.
    Feulvarch E, Moulin N, Saillard P, Lornage T, Bergheau J-M (2005) 3d simulation of glass forming process. J Mater Process Technol 164:1197–1203CrossRefGoogle Scholar
  7. 7.
    Giannopapa CG, Groot J (2011) Modeling the blow-blow forming process in glass container manufacturing: a comparison between computations and experiments. J Fluid Eng 133:1289–1309Google Scholar
  8. 8.
    Ryzhakov P, Garcia J, Oñate E (2016) Lagrangian finite element model for the 3d simulation of glass forming processes. Comput Struct (submitted)Google Scholar
  9. 9.
    NoGrid pointsBlow software. Accessed 16 Mar 2016
  10. 10.
    Idelsohn S, Oñate E, Del Pin F (2004) The particle finite element method: a powerful tool to solve incompressible flows with free-surfaces and breaking waves. Int J Numer Methods Eng 61:964–989MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    Oñate E, Idelsohn S, Del Pin F, Aubry R (2004) The particle finite element method: an overview. Int J Comput Methods 1:267–307CrossRefzbMATHGoogle Scholar
  12. 12.
    Ryzhakov P, Oñate E, Rossi R, Idelsohn S (2010) Lagrangian FE methods for coupled problems in fluid mechanics, 2nd edn. CIMNE. Barcelona, SpainGoogle Scholar
  13. 13.
    Dadvand P, Rossi R, Oñate E (2010) An object-oriented environment for developing finite element codes for multi-disciplinary applications. Arch Comput Methods Eng 17/3:253–297CrossRefzbMATHGoogle Scholar
  14. 14.
    Kratos multi-physcis. Accessed 16 Mar 2016
  15. 15.
    Seward III TP, Vascott T (2005) High temperature glass melt property database for process modeling. Wiley-American Ceramic Society Edition. Westerville, OhioGoogle Scholar
  16. 16.
    Osher SJ, Fedkiw RP (2006) Level set methods and dynamic implicit surfaces. Springer edition, BerlinzbMATHGoogle Scholar
  17. 17.
    Hirt CW, Nichols BD (1981) Volume of fluid (VOF) method for the dynamics of free boundaries. Comput Phys 39:201–225CrossRefzbMATHGoogle Scholar
  18. 18.
    Tornberg A-K, Engquist B (2000) A finite element based level-set method for multiphase flow applications. Comput Vis Sci 3(1–2):93–101CrossRefzbMATHGoogle Scholar
  19. 19.
    Delaunay B (1934) Sur la sphere vide. Izvestia Akademii Nauk SSSR, Otdelenie Matematicheskikh i Estestvennykh Nauk 7:793–800zbMATHGoogle Scholar
  20. 20.
    Franci A, Cremonesi M (2016) Critical investigation of the particle finite element method. Part i: volume conservation with remeshing. Comput Particle Mech (CPM), 19/02/2016 (submitted)Google Scholar
  21. 21.
    Donea J, Huerta A (2003) Finite element method for flow problems. Wiley edition, Hoboken. John Wiley & Sons, ChichesterGoogle Scholar
  22. 22.
    Zienkiewicz OS, Taylor RL, Nithiarasu P (2009) The finite element method for fluid dynamics. 6th edn, 3 volumes. Elsevier Butterworth-Heinemann edition. Oxford, KidlingtonGoogle Scholar
  23. 23.
    Brezzi F, Bathe K-J (1990) A discourse on the stability of the mixed finite element formulations. J Comput Methods Appl Mech 22:27–57MathSciNetCrossRefzbMATHGoogle Scholar
  24. 24.
    Ryzhakov P, Rossi R, Idelsohn S, Oñate E (2010) A monolithic Lagrangian approach for fluid-structure interaction problems. J Comput Mech 46/6:883–899MathSciNetCrossRefzbMATHGoogle Scholar
  25. 25.
    Yanenko NN (1971) The method of fractional steps. The solution of problems of mathematical physics in several variables. Springer edition, translated from Russian by Cheron TGoogle Scholar
  26. 26.
    Chorin AJ (1967) A numerical method for solving incompressible viscous problems. J Comput Phys 2:12–26CrossRefzbMATHGoogle Scholar
  27. 27.
    Ryzhakov P, Oñate E, Rossi R, Idelsohn S (2012) Improving mass conservation in simulation of incompressible flows. Int J Numer Methods Eng 90/12:1435–1451MathSciNetCrossRefzbMATHGoogle Scholar
  28. 28.
    Idelsohn S, Oñate E (2010) The challenge of mass conservation in the solution of free-surface flows with the fractional-step method. Int J Numer Methods Biomed Eng 26:1313–1330MathSciNetCrossRefzbMATHGoogle Scholar
  29. 29.
    Ryzhakov P (2016) A modified fractional step method for fluid-structure interaction problems. Revista Intern. Met. Num. Ing. (RIMNI). doi: 10.106/j.rimni.2015.09.002 Google Scholar
  30. 30.
    Ryzhakov P, Cotela J, Rossi R, Oñate E (2014) A two-step monolithic method for the efficient simulation of incompressible flows. Int J Numer Methods Fluids 74(12):919–934MathSciNetCrossRefGoogle Scholar
  31. 31.
    Akkiraju N, Edelsbrunner H, Facello M, Fu P, Mucke E. P, Varela C (1995) Alpha shapes: definition and software. In: Proceedings of international computational geometry software workshopGoogle Scholar
  32. 32.
    Ryzhakov PB, Jarauta A, Secanell M, Pons-Prats J (2016) On the application of the PFEM to droplet dynamics modeling in fuel cells. Comp Part Mech, 1–11. doi: 10.1007/s40571-016-0112-9

Copyright information

© OWZ 2016

Authors and Affiliations

  1. 1.Centre Internacional de Mètodes Numèrics en Enginyeria (CIMNE)BarcelonaSpain

Personalised recommendations