{"title":"Connecting rate-dependent loading and relaxation behaviors of glassy polymers by fractional models","authors":"Zhouquan Wang, Wei Cai, Changyu Liu, Leixiao Wu","doi":"10.1007/s00707-024-04038-2","DOIUrl":null,"url":null,"abstract":"<div><p>In this paper, a fractional constitutive model is constructed to link the rate-dependent loading and relaxation stages. As for strain rate effects, an inverse relationship between relaxation time and strain rate is established with assuming fractional order following the microbial growth curve in the loading stage. The anomalous stress relaxation behaviors of glassy polymers under various strain rates are successfully characterized by establishing the relationship between model parameters and initial stress. The proposed model is validated by numerical results applied to various strain rates and initial relaxation strains. Compared with the existing model, the proposed fractional model presents higher accuracy.</p></div>","PeriodicalId":456,"journal":{"name":"Acta Mechanica","volume":"235 10","pages":"6169 - 6179"},"PeriodicalIF":2.3000,"publicationDate":"2024-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Acta Mechanica","FirstCategoryId":"5","ListUrlMain":"https://link.springer.com/article/10.1007/s00707-024-04038-2","RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MECHANICS","Score":null,"Total":0}
引用次数: 0
Abstract
In this paper, a fractional constitutive model is constructed to link the rate-dependent loading and relaxation stages. As for strain rate effects, an inverse relationship between relaxation time and strain rate is established with assuming fractional order following the microbial growth curve in the loading stage. The anomalous stress relaxation behaviors of glassy polymers under various strain rates are successfully characterized by establishing the relationship between model parameters and initial stress. The proposed model is validated by numerical results applied to various strain rates and initial relaxation strains. Compared with the existing model, the proposed fractional model presents higher accuracy.
期刊介绍：
Since 1965, the international journal Acta Mechanica has been among the leading journals in the field of theoretical and applied mechanics. In addition to the classical fields such as elasticity, plasticity, vibrations, rigid body dynamics, hydrodynamics, and gasdynamics, it also gives special attention to recently developed areas such as non-Newtonian fluid dynamics, micro/nano mechanics, smart materials and structures, and issues at the interface of mechanics and materials. The journal further publishes papers in such related fields as rheology, thermodynamics, and electromagnetic interactions with fluids and solids. In addition, articles in applied mathematics dealing with significant mechanics problems are also welcome.
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