{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,16]],"date-time":"2026-07-16T02:03:17Z","timestamp":1784167397305,"version":"3.55.0"},"reference-count":42,"publisher":"MDPI AG","issue":"14","license":[{"start":{"date-parts":[[2026,7,15]],"date-time":"2026-07-15T00:00:00Z","timestamp":1784073600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Polymers"],"abstract":"<jats:p>The ride stability and driving comfort of vehicles are highly dependent on the performance of the damping system. The fatigue life prediction of damping components using rubber as the core damping material has become a research hotspot in the field of vehicle vibration isolation. Taking an automotive engine rubber isolator as the research carrier, this paper jointly carries out finite element simulation analysis and structural component fatigue life tests. A dual-parameter mapping framework is proposed, which integrates maximum strain energy density and cyclic energy dissipation instead of using a single damage indicator. This approach comprehensively accounts for the coupling effect of energy storage and energy dissipation coexisting under actual service conditions. Through uniaxial tensile tests on rubber specimens, combined with finite element simulations and physical model parameters, a quantitative mapping relationship between laboratory specimens and full-scale engine rubber isolators is established. Based on this mapping, the fatigue life curve of the isolator is derived from the specimen-based failure characteristics. Validation tests under two randomly selected operating conditions yield prediction errors of 7.5% and 6.9%, demonstrating that the proposed model can accurately achieve equivalent fatigue life transformation from small specimens to actual components. Unlike conventional direct extrapolation methods, this approach does not require complex multiaxial fatigue tests on the component itself; it only needs simple specimen fatigue data, significantly reducing development costs, while providing a reliable theoretical basis for material selection, fatigue performance optimization, and forward structural design of rubber isolators.<\/jats:p>","DOI":"10.3390\/polym18141732","type":"journal-article","created":{"date-parts":[[2026,7,16]],"date-time":"2026-07-16T01:05:07Z","timestamp":1784163907000},"page":"1732","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Fatigue Life Mapping of Rubber Isolators Based on Maximum Strain Energy Density and Cyclic Energy Dissipation Criteria with Specimen Data"],"prefix":"10.3390","volume":"18","author":[{"given":"Yupeng","family":"Du","sequence":"first","affiliation":[{"name":"College of Electromechanical Engineering, North University of China, Taiyuan 030051, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3973-7793","authenticated-orcid":false,"given":"Jinying","family":"Huang","sequence":"additional","affiliation":[{"name":"College of Mechanical Engineering, North University of China, Taiyuan 030051, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Zhenfang","family":"Fan","sequence":"additional","affiliation":[{"name":"College of Mechanical Engineering, North University of China, Taiyuan 030051, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jiaolin","family":"Wei","sequence":"additional","affiliation":[{"name":"College of Mechanical Engineering, North University of China, Taiyuan 030051, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Wenwen","family":"Zhang","sequence":"additional","affiliation":[{"name":"College of Computer Science and Technology, North University of China, Taiyuan 030051, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Xiaolong","family":"Wang","sequence":"additional","affiliation":[{"name":"College of Mechanical Engineering, North University of China, Taiyuan 030051, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2026,7,15]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"293","DOI":"10.3901\/JME.2025.13.293","article-title":"Physically-data-driven Modeling Method for Fatigue Life Prediction of Natural Rubber","volume":"61","author":"Liu","year":"2025","journal-title":"J. Mech. Eng."},{"key":"ref_2","first-page":"1581","article-title":"Study on Effect of Engine Installation Metal Rubber Damper","volume":"29","author":"Deng","year":"2008","journal-title":"Acta Aeronaut. Astronaut. Sin."},{"key":"ref_3","first-page":"230","article-title":"Lifetime evaluation of rubber isolator for warship application","volume":"12","author":"Ding","year":"2010","journal-title":"J. Vib. Shock"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"111374","DOI":"10.1016\/j.measurement.2022.111374","article-title":"A Load Spectrum Editing Method of Time-frequency for Rubber Isolators Based on the Continuous Wavelet Transform","volume":"198","author":"Liu","year":"2022","journal-title":"Measurement"},{"key":"ref_5","first-page":"124","article-title":"Decoupling method for vibration isolation of automotive engine elastic supports","volume":"3","author":"Li","year":"2020","journal-title":"China Plant Eng."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"106","DOI":"10.1016\/j.polymer.2019.03.043","article-title":"Energy dissipation accompanying Mullins effect of nitrile butadiene rubber\/carbon black nanocomposites","volume":"171","author":"Li","year":"2019","journal-title":"Polymer"},{"key":"ref_7","first-page":"3","article-title":"FEM modeling of thermo-mechanical interaction in pre-pressed rubber block","volume":"14","author":"Pust","year":"2007","journal-title":"Eng. Mech."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"313","DOI":"10.1016\/j.cma.2004.03.014","article-title":"Approximating thermo-viscoelastic heating of largely strained solid rubber components","volume":"194","author":"Johnson","year":"2005","journal-title":"Comput. Methods Appl. Mech. Eng."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"949","DOI":"10.1016\/S0142-1123(02)00008-7","article-title":"A literature survey on fatigue analysis approaches for rubber","volume":"24","author":"Mars","year":"2002","journal-title":"Int. J. Fatigue"},{"key":"ref_10","first-page":"45","article-title":"Experiment and Fatigue Life Prediction of Filled Natural Rubber under Variable Amplitude Loading Conditions","volume":"52","author":"Duan","year":"2013","journal-title":"Chin. J. Mech. Eng."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"56","DOI":"10.3901\/JME.2012.10.056","article-title":"Study on prediction of fatigue life of rubber mount based on linear cumulative fatigue damage theory","volume":"48","author":"Wang","year":"2012","journal-title":"J. Mech. Eng."},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Wang, X., Sedaghati, R., Rakheja, S., and Shangguan, W. (2025). Rubber Fatigue Revisited: A State-of-the-Art Review Expanding on Prior Works by Tee, Mars and Fatemi. Polymers, 17.","DOI":"10.3390\/polym17070918"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"20228089","DOI":"10.1515\/epoly-2022-8089","article-title":"Study on the aging of three typical rubber materials under high- and low-temperature cyclic environment","volume":"23","author":"Li","year":"2023","journal-title":"e-Polymers"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"1287","DOI":"10.1007\/s10118-023-2948-9","article-title":"High-temperature thermo-oxidative aging of vulcanized natural rubber nanocomposites: Evolution of microstructure and mechanical properties","volume":"41","author":"Li","year":"2023","journal-title":"Chin. J. Polym. Sci."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"65","DOI":"10.1016\/j.matdes.2014.01.035","article-title":"Experiment and modeling of uniaxial tension fatigue performances for filled natural rubbers","volume":"58","author":"Shangguan","year":"2014","journal-title":"Mater. Des."},{"key":"ref_16","first-page":"48","article-title":"Numerical Study on Fatigue Life of Brush Seal Based on Miner\u2019s Linear Cumulative Damage Theory","volume":"48","author":"Liu","year":"2023","journal-title":"Lubr. Eng."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"A159","DOI":"10.1115\/1.4009458","article-title":"Cumulative damage in fatigue","volume":"12","author":"Miner","year":"1945","journal-title":"J. Appl. Mech."},{"key":"ref_18","first-page":"897","article-title":"Strain-based criterion for uniaxial fatigue life prediction for an SBR rubber: Comparative study and development","volume":"234","author":"Belkhiria","year":"2020","journal-title":"Proc. Inst. Mech. Eng. Part L J. Mater. Des. Appl."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"2288","DOI":"10.1007\/s11668-022-01502-w","article-title":"A study on fatigue life of marine isolation rubber based on crack initiation method","volume":"22","author":"Zhu","year":"2022","journal-title":"J. Fail. Anal. Prev."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"168","DOI":"10.1016\/j.ijfatigue.2014.03.026","article-title":"Multiaxial fatigue life predictors for rubbers: Application of recent developments to a carbon-filled SBR","volume":"66","author":"Ayoub","year":"2014","journal-title":"Int. J. Fatigue"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"104588","DOI":"10.1016\/j.mechmat.2023.104588","article-title":"Fatigue damage criteria for antivibration systems with filled natural rubber under negative and positive R ratios","volume":"179","author":"Robert","year":"2023","journal-title":"Mech. Mater."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"291","DOI":"10.1002\/pol.1953.120100303","article-title":"Rupture of Rubber. I. Characteristic Energy for Tearing","volume":"10","author":"Rivlin","year":"1953","journal-title":"J. Polym. Sci."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"1231","DOI":"10.1016\/j.ijfatigue.2007.08.015","article-title":"Fatigue Life Analysis and Predictions for NR and SBR under Variable Amplitude and Multiaxial Loading Conditions","volume":"30","author":"Harbour","year":"2008","journal-title":"Int. J. Fatigue"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"267","DOI":"10.1111\/j.1460-2695.2005.00989.x","article-title":"Prediction of Rubber Fatigue Life under Multiaxial Loading","volume":"29","author":"Zine","year":"2006","journal-title":"Fatigue Fract. Eng. Mater. Struct."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"527","DOI":"10.2298\/TSCI120503189B","article-title":"Prediction of heat generation in rubber or rubber-metal springs","volume":"16","author":"Miltenovic","year":"2012","journal-title":"Therm. Sci."},{"key":"ref_26","unstructured":"Ro, H.S. (1989). Modeling and Interpretation of Fatigue Failure Initiation in Rubber Related to Pneumatic Tires. [Ph.D. Thesis, Purdue University]."},{"key":"ref_27","first-page":"25","article-title":"Residual deformation evolution and energy dissipation characteristics of jute fiber\/polyethylene composites under cyclic loading","volume":"37","author":"Wang","year":"2019","journal-title":"Tech. Text."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"e202406937","DOI":"10.1002\/anie.202406937","article-title":"Hyperbranched Vitrimer for Ultrahigh Energy Dissipation Angew","volume":"63","author":"Lin","year":"2024","journal-title":"Chem. Int. Ed."},{"key":"ref_29","first-page":"28","article-title":"Bending energy dissipation mechanism of glass fiber\/resin composite foam sandwich panel","volume":"15","author":"Zhou","year":"2020","journal-title":"Chin. J. Ship Res."},{"key":"ref_30","first-page":"13","article-title":"Analysis of Split Tensile Mechanical Properties and Energy Dissipation of GF\/VE Composites","volume":"53","author":"Wang","year":"2025","journal-title":"Plast. Sci. Technol."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"58","DOI":"10.3901\/JME.2010.22.058","article-title":"Analysis of fatigue crack growth life for rubber vibration damper","volume":"46","author":"Ding","year":"2010","journal-title":"Mech. Eng."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"933","DOI":"10.1520\/JTE20180666","article-title":"Fatigue Crack Initiation Life Prediction of the Rubber Damper Based on Seq-N Curve of Rubber Material","volume":"49","author":"Dong","year":"2021","journal-title":"J. Test. Eval."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"e201900340","DOI":"10.1002\/zamm.201900340","article-title":"Dissipation energy based parameter identification of anisotropic linear viscoelastic composites","volume":"100","author":"Mika","year":"2020","journal-title":"Z. Angew. Math. Mech."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"307","DOI":"10.1111\/ffe.12908","article-title":"Continuous Fatigue Damage Prediction of a Rubber Fibre Composite Structure Using MultiaxialEnergy-based Approach","volume":"42","author":"Gosar","year":"2019","journal-title":"Fatigue Fract. Eng. Mater. Struct."},{"key":"ref_35","first-page":"30","article-title":"Advances in data-driven models for fatigue life prediction of metallic materials","volume":"55","author":"Gan","year":"2025","journal-title":"Adv. Mech."},{"key":"ref_36","doi-asserted-by":"crossref","unstructured":"Tobajas, R., Elduque, D., Ibarz, E., Javierre, C., and Gracia, L. (2020). A new multiparameter model for multiaxial fatigue life prediction ofrubber materials. Polymers, 12.","DOI":"10.3390\/polym12051194"},{"key":"ref_37","unstructured":"Mark, J.E., Erman, B., and Roland, C.M. (2013). The Science and Technology of Rubber, Academic Press. [4th ed.]."},{"key":"ref_38","unstructured":"Ferry, J.D. (1980). Viscoelastic Properties of Polymers, John Wiley & Sons. [3rd ed.]. Available online: https:\/\/www.wiley.com\/en-cn\/Viscoelastic+Properties+of+Polymers%2C+3rd+Edition-p-9780471048947."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"109646","DOI":"10.1016\/j.engfracmech.2023.109646","article-title":"Temperature dependent tensile fracture strength model of rubber materials based on Mooney-Rivlin model","volume":"292","author":"Yao","year":"2023","journal-title":"Eng. Fract. Mech."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"3670","DOI":"10.1002\/app.27141","article-title":"Damping characteristics of chlorobutyl rubber\/poly (ethyl acrylate)\/piezoelectric ceramic\/carbon black composites","volume":"108","author":"Liu","year":"2008","journal-title":"J. Appl. Polym. Sci."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"181","DOI":"10.1016\/0045-7949(87)90248-3","article-title":"A 3-D rubber material model verified in a user-supplied subroutine","volume":"26","author":"Peeken","year":"1987","journal-title":"Comput. Struct."},{"key":"ref_42","doi-asserted-by":"crossref","unstructured":"Qiu, X., Yin, H., and Xing, Q. (2022). Research progress on fatigue life of rubber materials. Polymers, 14.","DOI":"10.3390\/polym14214592"}],"container-title":["Polymers"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-4360\/18\/14\/1732\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,7,16]],"date-time":"2026-07-16T01:12:39Z","timestamp":1784164359000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-4360\/18\/14\/1732"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,7,15]]},"references-count":42,"journal-issue":{"issue":"14","published-online":{"date-parts":[[2026,7]]}},"alternative-id":["polym18141732"],"URL":"https:\/\/doi.org\/10.3390\/polym18141732","relation":{},"ISSN":["2073-4360"],"issn-type":[{"value":"2073-4360","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,7,15]]}}}