{"title":"Microbiology-inspired nonlinear variable-order fractional model for amorphous glassy polymer","authors":"Wei Cai, Zhouquan Wang, Yongqi Zhang, Changyu Liu","doi":"10.1007/s00707-024-04089-5","DOIUrl":null,"url":null,"abstract":"<div><p>In this paper, a variable-order fractional model is proposed to characterize the complex nonlinear temperature-dependent mechanical behaviors of amorphous glassy polymers, which play a crucial role in the wide applications. At a specific temperature, the variable order is defined to follow the microbial growth curve, which is consisted of a logarithmic growth stage and decay stage. The two stages are naturally connected on the conception that the growth rate is approaching to 0. The variable order is further physically interpreted based on microscopic mechanism. Furthermore, the relationships between elastic modulus, relaxation time and temperature are incorporated into the established model to demonstrate the temperature dependence. Various experimental results are observed to be well characterized by the proposed model, which validates the rationality and reliability. The predictive ability of the proposed model is also explored to verify its effectiveness.</p></div>","PeriodicalId":456,"journal":{"name":"Acta Mechanica","volume":"235 12","pages":"7027 - 7038"},"PeriodicalIF":2.3000,"publicationDate":"2024-09-14","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/s00707-024-04089-5","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 variable-order fractional model is proposed to characterize the complex nonlinear temperature-dependent mechanical behaviors of amorphous glassy polymers, which play a crucial role in the wide applications. At a specific temperature, the variable order is defined to follow the microbial growth curve, which is consisted of a logarithmic growth stage and decay stage. The two stages are naturally connected on the conception that the growth rate is approaching to 0. The variable order is further physically interpreted based on microscopic mechanism. Furthermore, the relationships between elastic modulus, relaxation time and temperature are incorporated into the established model to demonstrate the temperature dependence. Various experimental results are observed to be well characterized by the proposed model, which validates the rationality and reliability. The predictive ability of the proposed model is also explored to verify its effectiveness.
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.