{"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.
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.