# Prestrain-dependent viscosity of a highly filled elastomer: experiments and modeling

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## Abstract

Highly filled elastomers exhibit a complex microstructure made up of rigid fillers bounded by a thin layer polymeric matrix. The interactions between the fillers and the binder amplify locally the applied strains and induce a nonlinear viscoelastic behavior. The aim here is to analyze the influence of prestrain on the viscoelastic behavior. This paper proposes a prestrain-dependent viscoelastic constitutive model. The model is a superposition of three relaxation spectra, each corresponding to a family of polymer chains, and can be regarded in either its continuous or discrete expression. More specifically, one of these relaxation spectra is modified to assure the prestrain sensitivity. The parameters of the discrete model are identified from relaxation and DMA experiments performed on a solid propellant, and the obtained predictions match closely the experiments. The novelty of the analysis proposed in this paper is threefold. On the one hand, we report a new series of experimental measures, performed for a large range of frequencies for the DMA experiment and relaxation times for the relaxation experiment, and, on the other hand, we propose a constitutive law compatible with the principles of thermodynamics, which predicts closely the measurements. Finally, the analysis is performed comparing both relaxation and DMA experiments using the spectrum of relaxation times. A peculiarity of the present discussion is the novel identification method used, which identifies directly the relaxation times. This technique leads to models with smaller and optimum numbers of parameters than classical methods based on a logarithmic distribution of relaxation times.

## Keywords

Prestrain Time spectrum of relaxation Nonlinear viscoelasticity Constitutive behavior## Notes

### Acknowledgements

The authors would like to thank the Direction Générale de l’Armement, especially Laurent Munier (DGA), and HERAKLES-SAFRAN for financial support for this study.

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