Abstract
This chapter is devoted to a summary of the so-called extended non-affine tube model. First, general model approaches for representation of the behavior of elastomers within numerical simulations are discussed. Second, the extended non-affine tube model is considered in the context of hyperelastic material models. Starting from molecular-statistical considerations, a Helmholtz free energy function is derived and formulated in terms of continuum mechanical quantities of the macroscale. Furthermore, combination with a model approach to represent continuum damage and time-dependent effects is addressed. The free energy function of the model approach is further set into the context of thermomechanics to account for temperature-dependent behavior of elastomers within numerical simulations. Finally, finite element implementation of the extended non-affine tube model and its application to uniaxial and biaxial tension tests performed on elastomer specimens are presented.
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Acknowledgements
Some of the research results reported herein are partially supported by the Deutsche Forschungsgemeinschaft (DFG) under grant KA 1163/16. The financial support is gratefully acknowledged. The authors thank J.-B. Le Cam (IFMA, France) and his research group for their experimental-numerical cooperation.
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Behnke, R., Kaliske, M. (2016). The Extended Non-affine Tube Model for Crosslinked Polymer Networks: Physical Basics, Implementation, and Application to Thermomechanical Finite Element Analyses. In: Stöckelhuber, K., Das, A., Klüppel, M. (eds) Designing of Elastomer Nanocomposites: From Theory to Applications. Advances in Polymer Science, vol 275. Springer, Cham. https://doi.org/10.1007/12_2016_9
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