The Folgar–Tucker Model as a Differential Algebraic System for Fiber Orientation Calculation

• The Folgar-Tucker equation (FTE) is the model most frequently used for the prediction of fiber orientation (FO) in simulations of the injection molding process for short-fiber reinforced thermoplasts. In contrast to its widespread use in injection molding simulations, little is known about the mathematical properties of the FTE: an investigation of e.g. its phase spaceMFT has been presented only recently. The restriction of the dependent variable of the FTE to the setMFT turns the FTE into a differential algebraic system (DAS), a fact which is commonly neglected when devising numerical schemes for the integration of the FTE. In this article1 we present some recent results on the problem of trace stability as well as some introductory material which complements our recent paper.

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Author: Joachim Linn urn:nbn:de:hbz:386-kluedo-13808 Berichte des Fraunhofer-Instituts für Techno- und Wirtschaftsmathematik (ITWM Report) (75) Report English 2005 2005 Fraunhofer-Institut für Techno- und Wirtschaftsmathematik 2005/07/05 Folgar-Tucker model ; algebraic constraints ; fiber orientation ; invariants ; phase space ; trace stability Fraunhofer (ITWM) 5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik Standard gemäß KLUEDO-Leitlinien vor dem 27.05.2011

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