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Published on: May 18, 2015
Nonlinear Hyper-Viscoelastic Constitutive Modeling and PRF Parameter Identification of Rubber Materials
Mingkuan Wang1, Jiaheng Yao1, Long Zhang1
1College of Mechanical and Transportation Engineering, China University of Petroleum (Beijing), Beijing 102249, China.
Polymers
|July 28, 2026
Summary
This study develops an advanced constitutive model to accurately predict the nonlinear viscoelastic behavior of fluororubber (FKM) and hydrogenated nitrile rubber (HNBR) under large deformations and stress relaxation. The Ogden hyperelastic model combined with an optimized nonlinear parallel rheological framework (PRF) model provides reliable predictions for rubber materials.
Area of Science:
- Materials Science
- Mechanical Engineering
- Polymer Physics
Background:
- Rubber materials like fluororubber (FKM) and hydrogenated nitrile rubber (HNBR) exhibit complex nonlinear hyper-viscoelastic behavior under large deformations.
- Accurate constitutive models are crucial for predicting the performance and durability of rubber components in engineering applications, especially under stress relaxation conditions.
Purpose of the Study:
- To develop and validate a robust constitutive model for characterizing the nonlinear hyper-viscoelastic mechanical behavior of FKM and HNBR with varying hardness levels.
- To evaluate the efficacy of different hyperelastic models and optimize a parallel rheological framework (PRF) model for large deformation and stress relaxation scenarios.
Main Methods:
- Uniaxial mechanical tests and stress relaxation experiments were conducted on FKM and HNBR samples.
- Hyperelastic models (Neo-Hookean, Mooney-Rivlin, Yeoh, Ogden, Arruda-Boyce, Van der Waals) were evaluated, with the Ogden model (N=3) selected for its accuracy.
- Prony series parameters were identified from relaxation data, and a linear PRF model was established and subsequently optimized using Isight and the Hooke-Jeeves algorithm for nonlinear behavior.
Main Results:
- The Ogden model (N=3) demonstrated high accuracy (R² from 0.9879 to 0.9948) in fitting large-deformation responses for both FKM and HNBR.
- The optimized nonlinear PRF model accurately predicted stress relaxation behavior, with low mean absolute percentage errors (e.g., 1.57% for FKM70, 2.16% for HNBR60).
Conclusions:
- The combined Ogden (N=3) hyperelastic model and the optimized nonlinear PRF model effectively capture the large-deformation and time-dependent viscoelastic responses of rubber materials.
- This constitutive modeling approach provides a reliable basis for finite element analysis and parameter calibration of rubber sealing structures.
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