Finite element approximation of stabilized mixed models in finite strain hyperelasticity involving displacements and stresses and/or pressure—An overview of alternatives.
Saved in:
| Title: | Finite element approximation of stabilized mixed models in finite strain hyperelasticity involving displacements and stresses and/or pressure—An overview of alternatives. |
|---|---|
| Authors: | Codina, Ramon1,2 (AUTHOR) ramon.codina@upc.edu, Castañar, Inocencio1 (AUTHOR), Baiges, Joan1,2 (AUTHOR) |
| Source: | International Journal for Numerical Methods in Engineering. 9/30/2024, Vol. 125 Issue 18, p1-32. 32p. |
| Subjects: | Finite element method, Geometry, Equations |
| Abstract: | This paper presents mixed finite element formulations to approximate the hyperelasticity problem using as unknowns the displacements and either stresses or pressure or both. These mixed formulations require either finite element spaces for the unknowns that satisfy the proper inf‐sup conditions to guarantee stability or to employ stabilized finite element formulations that provide freedom for the choice of the interpolating spaces. The latter approach is followed in this work, using the Variational Multiscale concept to derive these formulations. Regarding the tackling of the geometry, we consider both infinitesimal and finite strain problems, considering for the latter both an updated Lagrangian and a total Lagrangian description of the governing equations. The combination of the different geometrical descriptions and the mixed formulations employed provides a good number of alternatives that are all reviewed in this paper. [ABSTRACT FROM AUTHOR] |
| Copyright of International Journal for Numerical Methods in Engineering is the property of Wiley-Blackwell 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 |
|
Full text is not displayed to guests.
Login for full access.
|
|
| FullText | Links: – Type: pdflink Text: Availability: 1 |
|---|---|
| Header | DbId: egs DbLabel: Engineering Source An: 179045252 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
| IllustrationInfo | |
| Items | – Name: Title Label: Title Group: Ti Data: Finite element approximation of stabilized mixed models in finite strain hyperelasticity involving displacements and stresses and/or pressure—An overview of alternatives. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Codina%2C+Ramon%22">Codina, Ramon</searchLink><relatesTo>1,2</relatesTo> (AUTHOR)<i> ramon.codina@upc.edu</i><br /><searchLink fieldCode="AR" term="%22Castañar%2C+Inocencio%22">Castañar, Inocencio</searchLink><relatesTo>1</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Baiges%2C+Joan%22">Baiges, Joan</searchLink><relatesTo>1,2</relatesTo> (AUTHOR) – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22International+Journal+for+Numerical+Methods+in+Engineering%22">International Journal for Numerical Methods in Engineering</searchLink>. 9/30/2024, Vol. 125 Issue 18, p1-32. 32p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Finite+element+method%22">Finite element method</searchLink><br /><searchLink fieldCode="DE" term="%22Geometry%22">Geometry</searchLink><br /><searchLink fieldCode="DE" term="%22Equations%22">Equations</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: This paper presents mixed finite element formulations to approximate the hyperelasticity problem using as unknowns the displacements and either stresses or pressure or both. These mixed formulations require either finite element spaces for the unknowns that satisfy the proper inf‐sup conditions to guarantee stability or to employ stabilized finite element formulations that provide freedom for the choice of the interpolating spaces. The latter approach is followed in this work, using the Variational Multiscale concept to derive these formulations. Regarding the tackling of the geometry, we consider both infinitesimal and finite strain problems, considering for the latter both an updated Lagrangian and a total Lagrangian description of the governing equations. The combination of the different geometrical descriptions and the mixed formulations employed provides a good number of alternatives that are all reviewed in this paper. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of International Journal for Numerical Methods in Engineering is the property of Wiley-Blackwell 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.) |
| PLink | https://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=egs&AN=179045252 |
| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1002/nme.7540 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 32 StartPage: 1 Subjects: – SubjectFull: Finite element method Type: general – SubjectFull: Geometry Type: general – SubjectFull: Equations Type: general Titles: – TitleFull: Finite element approximation of stabilized mixed models in finite strain hyperelasticity involving displacements and stresses and/or pressure—An overview of alternatives. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Codina, Ramon – PersonEntity: Name: NameFull: Castañar, Inocencio – PersonEntity: Name: NameFull: Baiges, Joan IsPartOfRelationships: – BibEntity: Dates: – D: 30 M: 09 Text: 9/30/2024 Type: published Y: 2024 Identifiers: – Type: issn-print Value: 00295981 Numbering: – Type: volume Value: 125 – Type: issue Value: 18 Titles: – TitleFull: International Journal for Numerical Methods in Engineering Type: main |
| ResultId | 1 |
