Numerical approximation of a thermodynamically complete rate‐type model for the elastic–perfectly plastic response

IF 2.3 4区 工程技术 Q1 MATHEMATICS, APPLIED
Pablo Alexei Gazca‐Orozco, Vít Průša, Karel Tůma
{"title":"Numerical approximation of a thermodynamically complete rate‐type model for the elastic–perfectly plastic response","authors":"Pablo Alexei Gazca‐Orozco, Vít Průša, Karel Tůma","doi":"10.1002/zamm.202300030","DOIUrl":null,"url":null,"abstract":"Abstract We analyse a numerical scheme for a system arising from a novel description of the standard elastic–perfectly plastic response. The elastic–perfectly plastic response is described via rate‐type equations that do not make use of the standard elastic‐plastic decomposition, and the model does not require the use of variational inequalities. Furthermore, the model naturally includes the evolution equation for temperature. We present a low order discretisation based on the finite element method. Under certain restrictions on the mesh we subsequently prove the existence of discrete solutions, and we discuss the stability properties of the numerical scheme. The analysis is supplemented with computational examples.","PeriodicalId":23924,"journal":{"name":"Zamm-zeitschrift Fur Angewandte Mathematik Und Mechanik","volume":" 3","pages":"0"},"PeriodicalIF":2.3000,"publicationDate":"2023-10-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Zamm-zeitschrift Fur Angewandte Mathematik Und Mechanik","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1002/zamm.202300030","RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0

Abstract

Abstract We analyse a numerical scheme for a system arising from a novel description of the standard elastic–perfectly plastic response. The elastic–perfectly plastic response is described via rate‐type equations that do not make use of the standard elastic‐plastic decomposition, and the model does not require the use of variational inequalities. Furthermore, the model naturally includes the evolution equation for temperature. We present a low order discretisation based on the finite element method. Under certain restrictions on the mesh we subsequently prove the existence of discrete solutions, and we discuss the stability properties of the numerical scheme. The analysis is supplemented with computational examples.
弹-完全塑性响应的热力学完全速率型模型的数值近似
摘要本文分析了一种由标准弹-完全塑性响应的新描述引起的系统的数值格式。弹塑性响应是通过不使用标准弹塑性分解的速率型方程来描述的,并且该模型不需要使用变分不等式。此外,该模型自然包含了温度的演化方程。提出了一种基于有限元法的低阶离散化方法。在一定的网格限制条件下,证明了离散解的存在性,并讨论了数值格式的稳定性。分析还附有算例。
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
CiteScore
3.30
自引率
8.70%
发文量
199
审稿时长
3.0 months
期刊介绍: ZAMM is one of the oldest journals in the field of applied mathematics and mechanics and is read by scientists all over the world. The aim and scope of ZAMM is the publication of new results and review articles and information on applied mathematics (mainly numerical mathematics and various applications of analysis, in particular numerical aspects of differential and integral equations), on the entire field of theoretical and applied mechanics (solid mechanics, fluid mechanics, thermodynamics). ZAMM is also open to essential contributions on mathematics in industrial applications.
×
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