Numerical Investigation of Gas Equations of State of the Isotropic Viscoelastic Polymer Membrane in Free and Confined Inflation

Abstract

In this work, we are interested in numerical simulation in free and confined inflation of a thin, isotropic and incompressible thermoplastic membrane, using the dynamic finite element method. Inflation of the membrane is controlled by the gas equation of state flowing into the enclosed volume. The dynamic pressure loading used in modeling is thus deduced from one of the three equations of state: the Redlich—Kwong, the van der Waals and the ideal equations. The viscoelastic behavior of the Lodge model is considered. The Lagrangian formulation, together with the assumption of the membrane theory, are used. The effect of the gas on the thickness and stress distribution, for the free and confined inflation (thermoforming process), is analyzed for these three gas equations of state.

Keywords

finite element viscoelastic gas equations of state free inflation thermoforming.

Get full access to this article

View all access options for this article.

References

Wiesche, S.A. (2004). Industrial Thermoforming Simulation of Automotive Fuel Tanks, Applied Thermal Engineering , 24: 2391—2409.

Warby, M.K. , Whiteman, J.R. , Jiang, W.G. , Warwick, P. and Wright, T. (2003). Finite Element Simulation of Thermoforming Processes for Polymer Sheet, Mathematics and Computer in Simulation . 61: 209—218.

Laroche, D. and Erchiqui, F. (1998). 3D Modeling of the Blow Moulding Process Simulation of Materials Processing: Theory, Methods and Applications, Huétink, J. and Baaijens, F. P. T. (eds), pp. 483—488, Balkema, Rotterdam, ISBN 90 5410 970 X.

Erchiqui, F. , Derdouri, A. , Gakwaya, A. and Verron, E. (2001). Analyse Experimentale et Numerique en Soufflage Libre d'une Membrane Thermoplastique, Entropie, No. 235/236, pp. 118—125.

Verron, E. , Marckmann, G. and Peseux, B. (2001). Dynamic Inflation of Non-Linear Elastic and Viscoelastic Rubberlike Membrane, International J. Numerical Methods Engineering , 50: 1233—1251.

Erchiqui, F. , and Diri, D. (2004). Modelisation du Comportement des Polymeres Thermoplastiques par une Approche Combinant la Méthode Dynamique des Éléments finis et la loi des gaz parfaits, Revue des Composites et des Matériaux Avancés , 13(1): 99—114.

Erchiqui, F. , Gakwaya, A. and Rachik, M. (2005). Dynamic Finite Element Analysis of Nonlinear Isotropic Hyperelastic and Viscoelastic Materials for Thermoforming Applications, Polymer Engineering & Science, 45(1): 125—134.

Zienkiewicz, O.C. and Taylor, R.L. (1991). The Finite Element Method, 4th edn, Vol. 1 and 2, McGraw-Hill, London .

Lodge, A.S. (1964). Elastic Liquids, Academic Press , London.

10.

Dokainish, M.A. and Subbaraj, K. (1989). A Survey of Direct Time-integration Methods in Computational Structural Dynamics, Comput. Struct ., 32(6): 1371—1386.

11.

Landau, D.L. and Lifshitz, E.M. (1984). Cours de Physique Théorique, Tome V, Physique Statistique, Editions MIR, Moscou .

12.

Redlich, O. and Kwong, J.N.S. (1949). On the Thermodynamics of Solution. V-An Equation of State, Chem. Rev., 44: 233—244.

13.

Ferry, J.D. (1980). Viscoelastic Properties of Polymer, John Wiley & Sons, New York.

14.

Macosko, C.W. (1994). Rheology: Principles, Measurements and Applications, John Wiley & Son, New York.

15.

DeLorenzi, H.G. and Nied, H.F. (1991). Finite Element Simulation of Thermoforming and Blow Molding, In: Progress in Polymer Processing, Isayev, A. L. (ed.), pp. 117—171. Hanser Publishers, Munich, Germany.