A rate-dependent endochronic approach to thermoplastic materials: temperature and filler volume fraction dependence Thomas Kletschkowski a, * , Uwe Schomburg a , Albrecht Bertram b a Technische Mechanik, Universita ¨ t der Bundeswehr Hamburg, Holstenhofweg 85, D-22043 Hamburg, Germany b Inst. f. Mechanik, Otto-von-Guericke-Universita ¨ t Magdeburg, Universita ¨ tsplatz 2, D-39106 Magdeburg, Germany Received 12 December 2003; received in revised form 18 May 2004 Abstract An endochronic viscoplastic approach, derived from the theory of finite viscoplasticity based on isomorphisms, is presented. The model allows to characterize viscoplastic material behaviour with equilibrium hysteresis using a rate- independent elastoplastic model with an endochronic flow rule and a logarithmic elastic law in parallel connection with a non-linear Maxwell model. The volumetric strains are assumed to be purely elastic. The proposed model describes the non-linear mechanical behaviour of thermoplastic materials such as filled polytetrafluoroethylene (PTFE). The temper- ature and filler volume fraction dependencies of the model parameters have been identified by a Levenberg–Marquardt algorithm. In contrast to previous suggestions, the proposed model is capable to describe both the non-linearities during strain controlled loading and the non-linearities during stress controlled unloading in a unified approach. The results of the numerical simulations are in fair agreement with the experimental data. Ó 2004 Elsevier Ltd. All rights reserved. Keywords: Endochronic theory of viscoplasticity; Thermoplastic materials; PTFE 1. Introduction Due to their mechanical properties thermoplas- tic materials are widely used in numerous engineer- ing applications. Typical examples are rotary shaft seals made of filled polytetrafluoroethylene (PTFE). The design engineer has to take into account the vis- coplastic material behaviour of these thermoplastic compounds, which is radically different from that of elastomeric materials. In the past, constitutive mod- els have been applied to simulate the mechanical re- sponse of thermoplastic materials, which had been successful only in particular load cases. 0167-6636/$ - see front matter Ó 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.mechmat.2004.06.003 * Corresponding author. Tel.: +49 40 6541 2282; fax: +49 40 6541 2822. E-mail address: kletsch@unibw-hamburg.de (T. Kletschkowski). Mechanics of Materials 37 (2005) 687–704 www.elsevier.com/locate/mechmat