{"title":"Radial Compression with Controlled Unloading of a Layered-Stratified Elastoplastic Hollow Sphere","authors":"D.V. Georgievskii","doi":"10.1134/S1061920825030070","DOIUrl":null,"url":null,"abstract":"<p> The stress-strain state arising after a two-stage spherically symmetric process “radial loading– partial unloading” in a hollow sphere (thick-walled spherical layer) nonuniform in radius is investigated. The inner boundary is fixed, and a radial compressive stress is applied to the outer boundary. The material of the sphere agrees with Ilyushin’s theory of small elastoplastic deformations. Both discontinuous and continuously stratified nonuniformity are admitted, while the bulk modulus of compression at all points of the material is assumed to be constant. At the first (intermediate) step, an excessive compression (over-compression) occurs, as a result of which the radius of the outer boundary becomes less than the required one. At the second step, where partial unloading occurs, the system is transferred to the required final position. Such a two-stage nature enables one to control the stress-strain state in the hollow sphere both as a whole and concerning its individual parameters. </p><p> <b> DOI</b> 10.1134/S1061920825030070 </p>","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":"32 3","pages":"480 - 484"},"PeriodicalIF":1.5000,"publicationDate":"2025-09-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Russian Journal of Mathematical Physics","FirstCategoryId":"101","ListUrlMain":"https://link.springer.com/article/10.1134/S1061920825030070","RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"PHYSICS, MATHEMATICAL","Score":null,"Total":0}
引用次数: 0
Abstract
The stress-strain state arising after a two-stage spherically symmetric process “radial loading– partial unloading” in a hollow sphere (thick-walled spherical layer) nonuniform in radius is investigated. The inner boundary is fixed, and a radial compressive stress is applied to the outer boundary. The material of the sphere agrees with Ilyushin’s theory of small elastoplastic deformations. Both discontinuous and continuously stratified nonuniformity are admitted, while the bulk modulus of compression at all points of the material is assumed to be constant. At the first (intermediate) step, an excessive compression (over-compression) occurs, as a result of which the radius of the outer boundary becomes less than the required one. At the second step, where partial unloading occurs, the system is transferred to the required final position. Such a two-stage nature enables one to control the stress-strain state in the hollow sphere both as a whole and concerning its individual parameters.
期刊介绍：
Russian Journal of Mathematical Physics is a peer-reviewed periodical that deals with the full range of topics subsumed by that discipline, which lies at the foundation of much of contemporary science. Thus, in addition to mathematical physics per se, the journal coverage includes, but is not limited to, functional analysis, linear and nonlinear partial differential equations, algebras, quantization, quantum field theory, modern differential and algebraic geometry and topology, representations of Lie groups, calculus of variations, asymptotic methods, random process theory, dynamical systems, and control theory.
求助内容：
应助结果提醒方式：
京公网安备 11010802042870号
