Skip to content
Licensed Unlicensed Requires Authentication Published by De Gruyter February 20, 2017

An Engineering Model that Simulates Pantographing Occurring in the Shaping Process of Reinforced Uncured Rubber Parts

  • B. Debbaut


When a material volume consisting of an uncured rubber matrix reinforced with two non-parallel sets of embedded reinforcement wires or cords is subjected to large deformations, pantographing may occur. In other words, the angles between reinforcement wires change. We introduce a simple phenomenological fluid model suitable for the numerical prediction of pantographing, as can be encountered in industrial processes such as the manufacturing of rubber tires or reinforced hoses. The reinforced material is described with an orthotropic continuous fluid model. Here the reinforcement wires or cords are accounted for by the orthotropy, whose direction is locally affected by the deformation undergone by the matrix, and is updated accordingly. The model is subsequently applied to the simulation of a sagging experiment, where the role of pantographing is illustrated.

*Correspondence address, Mail address: Benoit Debbaut, ANSYS Belgium s. a., Avenue Pasteur 4, B-1300 Wavre, Belgium, E-mail:


AvalosseT., AlsteensB. and LegatV., “Rotor Shape Design by Numerical Simulation: A New Way to Improve Dispersive and Distributive Mixing in Batch Mixers”, Elastomery, 9, 1624 (2005)Search in Google Scholar

ClemeurN., RutgersR. P. G. and DebbautB., “Numerical Simulation of Abrupt Contraction Flow Using the Double-Convected Pom-Pom Model”, J. Non-Newtonian Fluid Mech., 117, 193209 (2004) 10.1016/j.jnnfm.2004.02.001Search in Google Scholar

CrochetM.J., Debbaut, B., Keunings, R. and Marchal, J. M., “Chapter 2 POLYFLOW, A Multi-Purpose Finite Element Program for Continuous Polymer Flows”, in Applications of CAE in Extrusion and Other Continuous Processes, O’Brien, K. T. (Ed.), Hanser, München (1992)Search in Google Scholar

Debbaut, B., “Rheology: From Process to Simulation”, Plast. Rubber Compos., 37, 166173 (2008) 10.1179/174328908X283357Search in Google Scholar

Debbaut, B., “Numerical Simulation of Elastic Recovery for Uncured Rubber Compound with a Multi-Mode Simhambhatla-Leonov Model”, Chem. Eng. Sci., 64, 45804587 (2009) 10.1016/j.ces.2009.01.033Search in Google Scholar

Debbaut, B., “A Simple Model for Reinforced Rubber”, Proceeding of the NPD 2014 Conf., Chalmers University, Göteborg, 100101 (2014)Search in Google Scholar

Debbaut, B., “A Simple Model for Wire Reinforced Polymer and Rubber”, Rheol. Acta, 54, 403409 (2015) 10.1007/s00397-015-0840-4Search in Google Scholar

Gresho, P. M., Lee, R. L. and Sani, R. L.: Recent Advances in Numerical Methods in Fluids, Pineridge, Swansea (1980)Search in Google Scholar

Keunings, R., “An Algorithm for the Simulation of Transient Viscoelastic Flows with Free Surfaces”, J. Comput. Phys., 62, 165182 (1985)Search in Google Scholar

Kovak, F. J., “Chapter 14 Tire Manufacture and Engineering”, in Science and Technology of Rubber, Eirich, F. R. (Ed.), Academic Press, New York (1978) 10.1016/B978-0-12-234360-5.50019-5Search in Google Scholar

Lekhnitskii, S. G.: Theory of Elasticity of an Anisotropic Elastic Body, Holden-Day, New York (1963)Search in Google Scholar

Macosko, C. W.: Rheology: Principles, Measurements, Applications, J. Wiley & Sons, New York (1994)Search in Google Scholar

Simhambathla, M., Leonov, A. I., “On the Rheological Modelling of Filled Polymers with Particle-Matrix Interactions”, Rheol. Acta, 34, 329338 (1995) 10.1007/BF00367150Search in Google Scholar

Received: 2016-04-01
Accepted: 2016-05-26
Published Online: 2017-02-20
Published in Print: 2017-03-03

© 2017, Carl Hanser Verlag, Munich

Downloaded on 3.6.2023 from
Scroll to top button