{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,15]],"date-time":"2026-07-15T05:05:47Z","timestamp":1784091947598,"version":"3.55.0"},"reference-count":23,"publisher":"MDPI AG","issue":"14","license":[{"start":{"date-parts":[[2026,7,8]],"date-time":"2026-07-08T00:00:00Z","timestamp":1783468800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"the National Key Research and Development Program of China","award":["2023YFC3011300"],"award-info":[{"award-number":["2023YFC3011300"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Polymers"],"abstract":"<jats:p>To accurately characterize the nonlinear hyper-viscoelastic mechanical behavior of rubber materials under large deformation and stress relaxation conditions, this study investigates fluororubber (FKM) and hydrogenated nitrile rubber (HNBR) with different hardness levels through uniaxial mechanical tests and stress relaxation experiments. A constitutive parameter identification method based on hyperelastic models and the parallel rheological framework (PRF) model is established. First, several representative hyperelastic models, including the Neo-Hookean, Mooney\u2013Rivlin, Yeoh, Ogden, Arruda\u2013Boyce, and Van der Waals models, are comparatively evaluated. The results show that the Ogden model with (N = 3) provides the highest fitting accuracy for the large-deformation responses of FKM and HNBR with different hardness levels, with coefficients of determination (R2) ranging from 0.9879 to 0.9948. Subsequently, the Prony series parameters are identified from the stress relaxation data and converted into the initial parameters of the linear PRF model. To overcome the limitations of the linear PRF model in predicting nonlinear relaxation behavior, the PRF parameters are further optimized using the Isight data matching method combined with the Hooke\u2013Jeeves algorithm. Finite element validation demonstrates that the optimized nonlinear PRF model can accurately predict the stress relaxation behavior of both FKM and HNBR. The mean absolute percentage errors of FKM60, FKM70, and FKM80 are 2.67%, 1.57%, and 2.56%, respectively, while those of HNBR60, HNBR70, and HNBR80 are 2.16%, 2.72%, and 2.58%, respectively. These results indicate that the combination of the Ogden (N = 3) hyperelastic model and the optimized nonlinear PRF model can effectively describe the large-deformation and time-dependent viscoelastic responses of rubber materials, providing a reliable constitutive modeling basis for finite element analysis and parameter calibration of rubber sealing structures.<\/jats:p>","DOI":"10.3390\/polym18141687","type":"journal-article","created":{"date-parts":[[2026,7,8]],"date-time":"2026-07-08T14:27:23Z","timestamp":1783520843000},"page":"1687","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Nonlinear Hyper-Viscoelastic Constitutive Modeling and PRF Parameter Identification of Rubber Materials"],"prefix":"10.3390","volume":"18","author":[{"ORCID":"https:\/\/orcid.org\/0009-0004-1714-5668","authenticated-orcid":false,"given":"Mingkuan","family":"Wang","sequence":"first","affiliation":[{"name":"College of Mechanical and Transportation Engineering, China University of Petroleum (Beijing), Beijing 102249, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jiaheng","family":"Yao","sequence":"additional","affiliation":[{"name":"College of Mechanical and Transportation Engineering, China University of Petroleum (Beijing), Beijing 102249, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Long","family":"Zhang","sequence":"additional","affiliation":[{"name":"College of Mechanical and Transportation Engineering, China University of Petroleum (Beijing), Beijing 102249, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Ang","family":"Gao","sequence":"additional","affiliation":[{"name":"College of Mechanical and Transportation Engineering, China University of Petroleum (Beijing), Beijing 102249, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Enchao","family":"Zhang","sequence":"additional","affiliation":[{"name":"College of Mechanical and Transportation Engineering, China University of Petroleum (Beijing), Beijing 102249, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Shimin","family":"Zhang","sequence":"additional","affiliation":[{"name":"College of Mechanical and Transportation Engineering, China University of Petroleum (Beijing), Beijing 102249, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0902-5776","authenticated-orcid":false,"given":"Xiaoxiao","family":"Zhu","sequence":"additional","affiliation":[{"name":"College of Safety and Ocean Engineering, China University of Petroleum (Beijing), Beijing 102249, China"},{"name":"Key Laboratory of Oil and Gas Production Safety and Emergency Technology, Ministry of Emergency Management, Beijing 102249, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2026,7,8]]},"reference":[{"key":"ref_1","first-page":"483","article-title":"Macroscopic Constitutive Models of Hyperelastic Materials and Their Fitting","volume":"42","author":"Bai","year":"2025","journal-title":"Chin. 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