{"title":"纯微应力耗散过程对平面应变梯度塑性问题的影响","authors":"A. Borokinni, O. Fadodun, A. Akinola","doi":"10.2298/TAM171017002B","DOIUrl":null,"url":null,"abstract":". This article considers a plane strain gradient plasticity theory of the Gurtin–Anand model [M. Gurtin, L. Anand, A theory of strain gra- dient plasticity for isotropic, plastically irrotational materials Part I: Small deformations , J. Mech. Phys. Solids 53 (2005), 1624–1649] for an isotropic material undergoing small deformation in the absence of plastic spin. It is assumed that the system of microstresses is purely dissipative, so that the free energy reduces to a function of the elastic strain, while the microstresses are only related to the plastic strain rate and gradient of the plastic strain rate via the constitutive relations. The plane strain problem of the Gurtin–Anand model for a purely dissipative process gives rise to elastic incompressibility. A weak formulation of the flow rule is derived, making the plane strain problem suitable for finite element implementation.","PeriodicalId":44059,"journal":{"name":"Theoretical and Applied Mechanics","volume":"8 3 1","pages":"177-188"},"PeriodicalIF":0.7000,"publicationDate":"2018-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"An effect of a purely dissipative process of microstresses on plane strain gradient plasticity problems\",\"authors\":\"A. Borokinni, O. Fadodun, A. Akinola\",\"doi\":\"10.2298/TAM171017002B\",\"DOIUrl\":null,\"url\":null,\"abstract\":\". This article considers a plane strain gradient plasticity theory of the Gurtin–Anand model [M. Gurtin, L. Anand, A theory of strain gra- dient plasticity for isotropic, plastically irrotational materials Part I: Small deformations , J. Mech. Phys. Solids 53 (2005), 1624–1649] for an isotropic material undergoing small deformation in the absence of plastic spin. It is assumed that the system of microstresses is purely dissipative, so that the free energy reduces to a function of the elastic strain, while the microstresses are only related to the plastic strain rate and gradient of the plastic strain rate via the constitutive relations. The plane strain problem of the Gurtin–Anand model for a purely dissipative process gives rise to elastic incompressibility. A weak formulation of the flow rule is derived, making the plane strain problem suitable for finite element implementation.\",\"PeriodicalId\":44059,\"journal\":{\"name\":\"Theoretical and Applied Mechanics\",\"volume\":\"8 3 1\",\"pages\":\"177-188\"},\"PeriodicalIF\":0.7000,\"publicationDate\":\"2018-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Theoretical and Applied Mechanics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.2298/TAM171017002B\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"MECHANICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Theoretical and Applied Mechanics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.2298/TAM171017002B","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MECHANICS","Score":null,"Total":0}
An effect of a purely dissipative process of microstresses on plane strain gradient plasticity problems
. This article considers a plane strain gradient plasticity theory of the Gurtin–Anand model [M. Gurtin, L. Anand, A theory of strain gra- dient plasticity for isotropic, plastically irrotational materials Part I: Small deformations , J. Mech. Phys. Solids 53 (2005), 1624–1649] for an isotropic material undergoing small deformation in the absence of plastic spin. It is assumed that the system of microstresses is purely dissipative, so that the free energy reduces to a function of the elastic strain, while the microstresses are only related to the plastic strain rate and gradient of the plastic strain rate via the constitutive relations. The plane strain problem of the Gurtin–Anand model for a purely dissipative process gives rise to elastic incompressibility. A weak formulation of the flow rule is derived, making the plane strain problem suitable for finite element implementation.
期刊介绍:
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