The weakly nonlinear response and nonaffine interpretation of the Johnson–Segalman/Gordon–Schowalter model

Nabil Ramlawi, N. A. Bharadwaj, R. Ewoldt
{"title":"The weakly nonlinear response and nonaffine interpretation of the Johnson–Segalman/Gordon–Schowalter model","authors":"Nabil Ramlawi, N. A. Bharadwaj, R. Ewoldt","doi":"10.1122/8.0000122","DOIUrl":null,"url":null,"abstract":"We derive new analytical solutions for the non-affine Johnson-Segalman/Gordon-Schowalter (JS/GS) constitutive equation with a general relaxation kernel in medium-amplitude oscillatory shear (MAOS) deformation. The results show time-strain separable (TSS) nonlinearity, therefore providing new physically-meaningful interpretation to the heuristic TSS nonlinear parameter in MAOS (Martinetti & Ewoldt Phys. Fl. (2019)). The upper-convected, lower-convected, and corotational Maxwell models are all subsets of the results presented here. The model assumes that the microscale elements causing stress in the material slip compared to the continuum deformation. We introduce a visualization of the non-affine deformation field that acts on stress-generating elements to reinforce the physical interpretation of the JS/GS class of models. Finally, a case study is presented where previously published results, from fitting TSS models to MAOS data, can be re-interpreted based on the concept of non-affine motion of the JS/GS framework.","PeriodicalId":8472,"journal":{"name":"arXiv: Soft Condensed Matter","volume":"1 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2020-07-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"6","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv: Soft Condensed Matter","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1122/8.0000122","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 6

Abstract

We derive new analytical solutions for the non-affine Johnson-Segalman/Gordon-Schowalter (JS/GS) constitutive equation with a general relaxation kernel in medium-amplitude oscillatory shear (MAOS) deformation. The results show time-strain separable (TSS) nonlinearity, therefore providing new physically-meaningful interpretation to the heuristic TSS nonlinear parameter in MAOS (Martinetti & Ewoldt Phys. Fl. (2019)). The upper-convected, lower-convected, and corotational Maxwell models are all subsets of the results presented here. The model assumes that the microscale elements causing stress in the material slip compared to the continuum deformation. We introduce a visualization of the non-affine deformation field that acts on stress-generating elements to reinforce the physical interpretation of the JS/GS class of models. Finally, a case study is presented where previously published results, from fitting TSS models to MAOS data, can be re-interpreted based on the concept of non-affine motion of the JS/GS framework.
Johnson-Segalman / Gordon-Schowalter模型的弱非线性响应和非仿射解释
本文给出了具有广义松弛核的非仿射Johnson-Segalman/Gordon-Schowalter (JS/GS)中振幅振荡剪切(MAOS)变形本构方程的新解析解。结果显示时间-应变可分(TSS)非线性,从而为MAOS (Martinetti & Ewoldt Phys)中启发式TSS非线性参数提供了新的物理意义解释。Fl。(2019))。上对流、下对流和同向麦克斯韦模型都是本文给出的结果的子集。与连续变形相比,该模型假定引起材料滑移的微尺度应力因素。我们引入了作用于应力产生单元的非仿射变形场的可视化,以加强对JS/GS类模型的物理解释。最后,提出了一个案例研究,其中先前发表的结果,从拟合TSS模型到MAOS数据,可以基于JS/GS框架的非仿射运动概念重新解释。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
求助全文
约1分钟内获得全文 求助全文
来源期刊
自引率
0.00%
发文量
0
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
确定
请完成安全验证×
copy
已复制链接
快去分享给好友吧!
我知道了
右上角分享
点击右上角分享
0
联系我们:info@booksci.cn Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术官方微信