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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 a new constitutive model to accurately predict the nonlinear mechanical behavior of fluororubber (FKM) and hydrogenated nitrile rubber (HNBR) under large deformations and stress relaxation, crucial for engineering applications.
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 essential for predicting their performance in engineering applications, particularly 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.
- To evaluate the performance of various hyperelastic models and optimize a parallel rheological framework (PRF) model for accurate prediction of stress relaxation.
Main Methods:
- Uniaxial mechanical tests and stress relaxation experiments were conducted on FKM and HNBR with varying hardness levels.
- Hyperelastic models (Neo-Hookean, Mooney-Rivlin, Yeoh, Ogden, Arruda-Boyce, Van der Waals) were evaluated, followed by parameter identification for the Ogden model (N=3).
- Prony series parameters were identified and used to optimize a nonlinear parallel rheological framework (PRF) model using the Isight data matching method and Hooke-Jeeves algorithm.
Main Results:
- The Ogden model (N=3) demonstrated high accuracy (R²: 0.9879–0.9948) 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., FKM60: 2.67%, HNBR60: 2.16%).
Conclusions:
- The combined Ogden (N=3) hyperelastic model and optimized nonlinear PRF model effectively capture the large-deformation and time-dependent viscoelastic responses of rubber materials.
- This provides a reliable constitutive modeling foundation for finite element analysis and parameter calibration of rubber sealing structures.
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