{"title":"A Dugdale-Barenblatt model for elliptical orifice problem with asymmetric cracks in one-dimensional orthorhombic quasicrystals","authors":"Jing Zhang, Guanting Liu","doi":"10.1007/s10483-023-3027-8","DOIUrl":null,"url":null,"abstract":"<div><p>By means of Muskhelishvili’s method and the technique of generalized conformal mapping, the physical plane problems are transformed into regular mathematical problems in quasicrystals (QCs). The analytical solution of an elliptical orifice problem with asymmetric cracks in one-dimensional (1D) orthorhombic QCs is obtained. By using the Dugdale-Barenblatt model, the plastic simulation at the crack tip of the elliptical orifice with asymmetric cracks in 1D orthorhombic QCs is performed. Finally, the size of the atomic cohesive force zone is determined precisely, and the size of the atomic cohesive force zone around the crack tip of an elliptical orifice with a single crack or two symmetric cracks is obtained.</p></div>","PeriodicalId":55498,"journal":{"name":"Applied Mathematics and Mechanics-English Edition","volume":"44 9","pages":"1533 - 1546"},"PeriodicalIF":4.5000,"publicationDate":"2023-08-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Applied Mathematics and Mechanics-English Edition","FirstCategoryId":"5","ListUrlMain":"https://link.springer.com/article/10.1007/s10483-023-3027-8","RegionNum":2,"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
By means of Muskhelishvili’s method and the technique of generalized conformal mapping, the physical plane problems are transformed into regular mathematical problems in quasicrystals (QCs). The analytical solution of an elliptical orifice problem with asymmetric cracks in one-dimensional (1D) orthorhombic QCs is obtained. By using the Dugdale-Barenblatt model, the plastic simulation at the crack tip of the elliptical orifice with asymmetric cracks in 1D orthorhombic QCs is performed. Finally, the size of the atomic cohesive force zone is determined precisely, and the size of the atomic cohesive force zone around the crack tip of an elliptical orifice with a single crack or two symmetric cracks is obtained.
期刊介绍：
Applied Mathematics and Mechanics is the English version of a journal on applied mathematics and mechanics published in the People''s Republic of China. Our Editorial Committee, headed by Professor Chien Weizang, Ph.D., President of Shanghai University, consists of scientists in the fields of applied mathematics and mechanics from all over China.
Founded by Professor Chien Weizang in 1980, Applied Mathematics and Mechanics became a bimonthly in 1981 and then a monthly in 1985. It is a comprehensive journal presenting original research papers on mechanics, mathematical methods and modeling in mechanics as well as applied mathematics relevant to neoteric mechanics.
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