Thermo-mechanically coupled compatibility conditions in orthogonal curvilinear coordinates: equivalent temperature variation of initially stressed elastomers.
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| Title: | Thermo-mechanically coupled compatibility conditions in orthogonal curvilinear coordinates: equivalent temperature variation of initially stressed elastomers. |
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| Authors: | Zhang, Mengru1,2 (AUTHOR), Xu, Mingzhu1,2 (AUTHOR), Chen, Weiting1,2 (AUTHOR) chenweiting@imech.ac.cn, Zhao, Yapu1,2 (AUTHOR) |
| Source: | Applied Mathematics & Mechanics. Mar2025, Vol. 46 Issue 3, p423-446. 24p. |
| Subjects: | Steady state conduction, Curvilinear coordinates, Differential forms, Heat conduction, Path integrals |
| Abstract: | The initial stresses widely exist in elastic materials. While achieving a continuum stress-free configuration through compatible unloading is desirable, mechanical unloading alone frequently proves insufficient, posing challenges in avoiding virtual stress-free configurations. In this paper, we introduce a novel concept of equivalent temperature variation to counteract the incompatible initial strain. Our focus is on initially stressed cylindrical and spherical elastomers, where we first derive the Saint-Venant, Beltrami-Michell, and Volterra integral conditions in orthogonal curvilinear coordinates using the exterior differential form theory. It is shown that for any given axially or spherically distributed initial stress, an equivalent temperature variation always exists. Furthermore, we propose two innovative initial stress forms based on the steady-state heat conduction. By introducing an equivalent temperature variation, the initial stress can be released through a compatible thermo-mechanical unloading process, offering valuable insights into the constitutive theory of initially stressed elastic materials. [ABSTRACT FROM AUTHOR] |
| Copyright of Applied Mathematics & Mechanics is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) | |
| Database: | Engineering Source |
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| Header | DbId: egs DbLabel: Engineering Source An: 183286154 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: Thermo-mechanically coupled compatibility conditions in orthogonal curvilinear coordinates: equivalent temperature variation of initially stressed elastomers. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Zhang%2C+Mengru%22">Zhang, Mengru</searchLink><relatesTo>1,2</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Xu%2C+Mingzhu%22">Xu, Mingzhu</searchLink><relatesTo>1,2</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Chen%2C+Weiting%22">Chen, Weiting</searchLink><relatesTo>1,2</relatesTo> (AUTHOR)<i> chenweiting@imech.ac.cn</i><br /><searchLink fieldCode="AR" term="%22Zhao%2C+Yapu%22">Zhao, Yapu</searchLink><relatesTo>1,2</relatesTo> (AUTHOR) – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Applied+Mathematics+%26+Mechanics%22">Applied Mathematics & Mechanics</searchLink>. Mar2025, Vol. 46 Issue 3, p423-446. 24p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Steady+state+conduction%22">Steady state conduction</searchLink><br /><searchLink fieldCode="DE" term="%22Curvilinear+coordinates%22">Curvilinear coordinates</searchLink><br /><searchLink fieldCode="DE" term="%22Differential+forms%22">Differential forms</searchLink><br /><searchLink fieldCode="DE" term="%22Heat+conduction%22">Heat conduction</searchLink><br /><searchLink fieldCode="DE" term="%22Path+integrals%22">Path integrals</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: The initial stresses widely exist in elastic materials. While achieving a continuum stress-free configuration through compatible unloading is desirable, mechanical unloading alone frequently proves insufficient, posing challenges in avoiding virtual stress-free configurations. In this paper, we introduce a novel concept of equivalent temperature variation to counteract the incompatible initial strain. Our focus is on initially stressed cylindrical and spherical elastomers, where we first derive the Saint-Venant, Beltrami-Michell, and Volterra integral conditions in orthogonal curvilinear coordinates using the exterior differential form theory. It is shown that for any given axially or spherically distributed initial stress, an equivalent temperature variation always exists. Furthermore, we propose two innovative initial stress forms based on the steady-state heat conduction. By introducing an equivalent temperature variation, the initial stress can be released through a compatible thermo-mechanical unloading process, offering valuable insights into the constitutive theory of initially stressed elastic materials. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Applied Mathematics & Mechanics is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.) |
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| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1007/s10483-025-3230-9 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 24 StartPage: 423 Subjects: – SubjectFull: Steady state conduction Type: general – SubjectFull: Curvilinear coordinates Type: general – SubjectFull: Differential forms Type: general – SubjectFull: Heat conduction Type: general – SubjectFull: Path integrals Type: general Titles: – TitleFull: Thermo-mechanically coupled compatibility conditions in orthogonal curvilinear coordinates: equivalent temperature variation of initially stressed elastomers. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Zhang, Mengru – PersonEntity: Name: NameFull: Xu, Mingzhu – PersonEntity: Name: NameFull: Chen, Weiting – PersonEntity: Name: NameFull: Zhao, Yapu IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 03 Text: Mar2025 Type: published Y: 2025 Identifiers: – Type: issn-print Value: 02534827 Numbering: – Type: volume Value: 46 – Type: issue Value: 3 Titles: – TitleFull: Applied Mathematics & Mechanics Type: main |
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