<p>A hyper-visco-pseudo-elastic model of rubber is presented, which is applied to model various mechanical behaviors, including strain rate effect, temperature effect, and the Mullins effect. The proposed model combines the Yeoh hyperelastic model, the linear viscoelastic theory of Prony series, and the Ogden–Roxburgh pseudo-elastic material model. The temperature effect is reflected by associating relaxation time, relaxation amount, and pseudo-elastic parameters with temperature. To determine model parameters effectively through experiments, a numerical stress solution based on finite time increments is provided, allowing the incorporation of rubber experiments to obtain model parameters directly. Stress relaxation and loading and unloading experiments are conducted using ethylene propylene diene monomer (EPDM) rubber to validate the proposed model. The obtained experimental data are fitted using the numerical stress solution and the gray wolf optimization (GWO) algorithm, yielding the constitutive model parameters. The fitting accuracy is demonstrated by <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="396_2025_5411_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="21" /> </InlineMediaObject> <EquationSource Format="TEX">${R}^{2}$</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mrow> <mi>R</mi> </mrow> <mn>2</mn> </msup> </math></EquationSource> </InlineEquation> values exceeding 0.985 for all experimental curves. Furthermore, the model's predictive capability is evaluated by conducting experiments at temperatures different from the fitting temperature. The results exhibit <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="396_2025_5411_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="21" /> </InlineMediaObject> <EquationSource Format="TEX">${R}^{2}$</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mrow> <mi>R</mi> </mrow> <mn>2</mn> </msup> </math></EquationSource> </InlineEquation> values greater than 0.986 between the experimental and predicted curves. The good consistency of the results indicates that the proposed model has a high applicability potential, and it can fit material parameters with less experiments to predict the experimental outcomes under other working conditions.</p>

A hyper-visco-pseudo-elastic model to characterize the temperature-dependent behavior of ethylene propylene diene monomer rubber

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发表日期：

2025年4月10日

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Dianjie Jiang,
Zhiping Tu,
Zhanjiang Wang

摘要

A hyper-visco-pseudo-elastic model of rubber is presented, which is applied to model various mechanical behaviors, including strain rate effect, temperature effect, and the Mullins effect. The proposed model combines the Yeoh hyperelastic model, the linear viscoelastic theory of Prony series, and the Ogden–Roxburgh pseudo-elastic material model. The temperature effect is reflected by associating relaxation time, relaxation amount, and pseudo-elastic parameters with temperature. To determine model parameters effectively through experiments, a numerical stress solution based on finite time increments is provided, allowing the incorporation of rubber experiments to obtain model parameters directly. Stress relaxation and loading and unloading experiments are conducted using ethylene propylene diene monomer (EPDM) rubber to validate the proposed model. The obtained experimental data are fitted using the numerical stress solution and the gray wolf optimization (GWO) algorithm, yielding the constitutive model parameters. The fitting accuracy is demonstrated by ${R}^{2}$ $R^{2}$ values exceeding 0.985 for all experimental curves. Furthermore, the model's predictive capability is evaluated by conducting experiments at temperatures different from the fitting temperature. The results exhibit ${R}^{2}$ $R^{2}$ values greater than 0.986 between the experimental and predicted curves. The good consistency of the results indicates that the proposed model has a high applicability potential, and it can fit material parameters with less experiments to predict the experimental outcomes under other working conditions.