Recovery and continuity of surfaces with assigned director field.
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| Title: | Recovery and continuity of surfaces with assigned director field. |
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| Authors: | Malin, Maria1 (AUTHOR), Mardare, Cristinel2 (AUTHOR) cristinel.mardare@math.cnrs.fr |
| Source: | Mathematics & Mechanics of Solids. Mar2026, Vol. 31 Issue 3, p673-707. 35p. |
| Subjects: | Tensor fields, Elastic plates & shells, Function spaces, Micropolar elasticity, Geometric surfaces, Vector fields |
| Abstract: | We show that surfaces with assigned director field immersed in the three-dimensional Euclidean space can be defined intrinsically by four tensor fields, of which two are of order two, one of order one, and one of order zero. We then show how a surface and its assigned director field can be reconstructed from these four tensors and prove that the reconstruction operator is continuous between ad hoc functional spaces with as little regularity as possible. These results have applications in the Cosserat theory of nonlinearly elastic shells, the strain energy of which are defined precisely in terms of the four tensor fields defined in this paper. [ABSTRACT FROM AUTHOR] |
| Copyright of Mathematics & Mechanics of Solids is the property of Sage Publications Inc. 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 |
| FullText | Text: Availability: 0 |
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| Header | DbId: egs DbLabel: Engineering Source An: 192252378 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: Recovery and continuity of surfaces with assigned director field. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Malin%2C+Maria%22">Malin, Maria</searchLink><relatesTo>1</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Mardare%2C+Cristinel%22">Mardare, Cristinel</searchLink><relatesTo>2</relatesTo> (AUTHOR)<i> cristinel.mardare@math.cnrs.fr</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Mathematics+%26+Mechanics+of+Solids%22">Mathematics & Mechanics of Solids</searchLink>. Mar2026, Vol. 31 Issue 3, p673-707. 35p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Tensor+fields%22">Tensor fields</searchLink><br /><searchLink fieldCode="DE" term="%22Elastic+plates+%26+shells%22">Elastic plates & shells</searchLink><br /><searchLink fieldCode="DE" term="%22Function+spaces%22">Function spaces</searchLink><br /><searchLink fieldCode="DE" term="%22Micropolar+elasticity%22">Micropolar elasticity</searchLink><br /><searchLink fieldCode="DE" term="%22Geometric+surfaces%22">Geometric surfaces</searchLink><br /><searchLink fieldCode="DE" term="%22Vector+fields%22">Vector fields</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: We show that surfaces with assigned director field immersed in the three-dimensional Euclidean space can be defined intrinsically by four tensor fields, of which two are of order two, one of order one, and one of order zero. We then show how a surface and its assigned director field can be reconstructed from these four tensors and prove that the reconstruction operator is continuous between ad hoc functional spaces with as little regularity as possible. These results have applications in the Cosserat theory of nonlinearly elastic shells, the strain energy of which are defined precisely in terms of the four tensor fields defined in this paper. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Mathematics & Mechanics of Solids is the property of Sage Publications Inc. 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: 10.1177/10812865251413212 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 35 StartPage: 673 Subjects: – SubjectFull: Tensor fields Type: general – SubjectFull: Elastic plates & shells Type: general – SubjectFull: Function spaces Type: general – SubjectFull: Micropolar elasticity Type: general – SubjectFull: Geometric surfaces Type: general – SubjectFull: Vector fields Type: general Titles: – TitleFull: Recovery and continuity of surfaces with assigned director field. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Malin, Maria – PersonEntity: Name: NameFull: Mardare, Cristinel IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 03 Text: Mar2026 Type: published Y: 2026 Identifiers: – Type: issn-print Value: 10812865 Numbering: – Type: volume Value: 31 – Type: issue Value: 3 Titles: – TitleFull: Mathematics & Mechanics of Solids Type: main |
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