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Research Article | Open Access

A comparative study of 85 hyperelastic constitutive models for both unfilled rubber and highly filled rubber nanocomposite material

Hong Hea,b, Qiang Zhanga,b, Yaru Zhanga, Jianfeng Chena, Liqun Zhanga,c( ), Fanzhu Lia,c( )
State Key Laboratory of Organic-Inorganic Composites, Beijing University of Chemical Technology, Beijing, 100029, China
College of Mechanical and Electrical Engineering, Beijing University of Chemical Technology, Beijing, 100029, China
Key Laboratory of Beijing City on Preparation and Processing of Novel Polymer Materials, Beijing University of Chemical Technology, Beijing, 100029, China
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Abstract

Nonlinear finite element analysis is widely used for structural optimization of the design and the reliability analysis of complex elastomeric components. However, high-precision numerical results cannot be achieved without reliable strain energy functions (SEFs) of the rubber or rubber nanocomposite material. Although hyperelastic constitutive models have been studied for nearly 80 years, selecting one that accurately describes rubber's mechanical response is still a challenge. This work reviews 85 isotropic SEFs based on both the phenomenological theory and the micromechanical network theory proposed from the 1940s to 2019. A fitting algorithm which can realize the automatic fitting optimization and determination of the parameters of all SEFs reviewed is developed. The ability of each SEF to reproduce the experimental data of both the unfilled and highly filled rubber nanocomposite is quantitatively assessed based on a new proposed evaluation index. The top 30 SEFs for the unfilled rubber and the top 14 SEFs for the highly filled rubber nanocomposite are presented in the ranking lists. Finally, some suggestions on how to select an appropriate hyperelastic constitutive model are given, and the perspective on the future progress of constitutive models is summarized.

Keywords

Rubber-like materialsHyperelastic constitutive modelStrain energy functionPhenomenological modelMicromechanical network modelUHYPER subroutine

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Nano Materials Science
Volume 4 Issue 2,
June 2022
Pages 64-82
DOI: 10.1016/j.nanoms.2021.07.003
Cite this article:
He H, Zhang Q, Zhang Y, et al. A comparative study of 85 hyperelastic constitutive models for both unfilled rubber and highly filled rubber nanocomposite material. Nano Materials Science, 2022, 4(2): 64-82. https://doi.org/10.1016/j.nanoms.2021.07.003

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Received: 02 April 2021
Accepted: 21 June 2021
Published: 16 July 2021
© 2021 Chongqing University.

This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).
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