A mixed displacement-pressure-stress stabilized finite element formulation for a finite strain damage model.
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| Title: | A mixed displacement-pressure-stress stabilized finite element formulation for a finite strain damage model. |
|---|---|
| Authors: | Castañar, Inocencio1 (AUTHOR) inocencio.castanar@upc.edu, Codina, Ramon1,2,3 (AUTHOR) ramon.codina@upc.edu, Baiges, Joan2,3 (AUTHOR) joan.baiges@upc.edu |
| Source: | Computer Methods in Applied Mechanics & Engineering. Jun2026, Vol. 455, pN.PAG-N.PAG. 1p. |
| Subjects: | Finite element method, Damage models, Strain tensors, Nonlinear equations, Elastic deformation, Solid mechanics |
| Abstract: | In this work, we describe a finite element formulation for the approximation of solid mechanics problems using a damage model under finite strain conditions. The balance equations are written in a total Lagrangian framework, employing the deviatoric component of the second Piola–Kirchhoff stress tensor, the displacement, and the pressure as primary variables. Introducing the pressure as a variable enables the treatment of incompressible materials, while incorporating the stress improves the stress approximation, which is crucial when nonlinear material laws depending on stress (or strain) are considered. In particular, we adopt the damage model proposed by Comellas et al. (International Journal for Numerical Methods in Engineering, Vol. 105, pp. 781–800, 2016), which generalizes previous isotropic damage models from infinitesimal strains to finite ones. This damage model is combined with a hyperelastic formulation for the reversible component of the deformation. The three-field formulation we consider was first introduced and analyzed for the Stokes problem by Codina (SIAM Journal on Numerical Analysis, Vol. 47, pp. 699–718, 2009). The interest of interpolating stress as an independent variable was highlighted in the work of Cervera et al. (Computer Methods in Applied Mechanics and Engineering, Vol. 199, pp. 2559–2570, 2010), and has since been successfully applied to numerous problems involving both linear and nonlinear constitutive behavior under the small strain assumption. More recently, Codina et al. (International Journal for Numerical Methods in Engineering, Vol. 125, e7540, 2024), extended the three-field formulation to geometrically nonlinear problems. The purpose of the present work is to combine these approaches, addressing problems that involve both nonlinear constitutive laws and geometrical nonlinearity with a mixed, three-field approach. [ABSTRACT FROM AUTHOR] |
| Copyright of Computer Methods in Applied Mechanics & Engineering is the property of Elsevier B.V. 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: 192566863 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: A mixed displacement-pressure-stress stabilized finite element formulation for a finite strain damage model. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Castañar%2C+Inocencio%22">Castañar, Inocencio</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> inocencio.castanar@upc.edu</i><br /><searchLink fieldCode="AR" term="%22Codina%2C+Ramon%22">Codina, Ramon</searchLink><relatesTo>1,2,3</relatesTo> (AUTHOR)<i> ramon.codina@upc.edu</i><br /><searchLink fieldCode="AR" term="%22Baiges%2C+Joan%22">Baiges, Joan</searchLink><relatesTo>2,3</relatesTo> (AUTHOR)<i> joan.baiges@upc.edu</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Computer+Methods+in+Applied+Mechanics+%26+Engineering%22">Computer Methods in Applied Mechanics & Engineering</searchLink>. Jun2026, Vol. 455, pN.PAG-N.PAG. 1p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Finite+element+method%22">Finite element method</searchLink><br /><searchLink fieldCode="DE" term="%22Damage+models%22">Damage models</searchLink><br /><searchLink fieldCode="DE" term="%22Strain+tensors%22">Strain tensors</searchLink><br /><searchLink fieldCode="DE" term="%22Nonlinear+equations%22">Nonlinear equations</searchLink><br /><searchLink fieldCode="DE" term="%22Elastic+deformation%22">Elastic deformation</searchLink><br /><searchLink fieldCode="DE" term="%22Solid+mechanics%22">Solid mechanics</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: In this work, we describe a finite element formulation for the approximation of solid mechanics problems using a damage model under finite strain conditions. The balance equations are written in a total Lagrangian framework, employing the deviatoric component of the second Piola–Kirchhoff stress tensor, the displacement, and the pressure as primary variables. Introducing the pressure as a variable enables the treatment of incompressible materials, while incorporating the stress improves the stress approximation, which is crucial when nonlinear material laws depending on stress (or strain) are considered. In particular, we adopt the damage model proposed by Comellas et al. (International Journal for Numerical Methods in Engineering, Vol. 105, pp. 781–800, 2016), which generalizes previous isotropic damage models from infinitesimal strains to finite ones. This damage model is combined with a hyperelastic formulation for the reversible component of the deformation. The three-field formulation we consider was first introduced and analyzed for the Stokes problem by Codina (SIAM Journal on Numerical Analysis, Vol. 47, pp. 699–718, 2009). The interest of interpolating stress as an independent variable was highlighted in the work of Cervera et al. (Computer Methods in Applied Mechanics and Engineering, Vol. 199, pp. 2559–2570, 2010), and has since been successfully applied to numerous problems involving both linear and nonlinear constitutive behavior under the small strain assumption. More recently, Codina et al. (International Journal for Numerical Methods in Engineering, Vol. 125, e7540, 2024), extended the three-field formulation to geometrically nonlinear problems. The purpose of the present work is to combine these approaches, addressing problems that involve both nonlinear constitutive laws and geometrical nonlinearity with a mixed, three-field approach. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Computer Methods in Applied Mechanics & Engineering is the property of Elsevier B.V. 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: 10.1016/j.cma.2026.118868 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 1 StartPage: N.PAG Subjects: – SubjectFull: Finite element method Type: general – SubjectFull: Damage models Type: general – SubjectFull: Strain tensors Type: general – SubjectFull: Nonlinear equations Type: general – SubjectFull: Elastic deformation Type: general – SubjectFull: Solid mechanics Type: general Titles: – TitleFull: A mixed displacement-pressure-stress stabilized finite element formulation for a finite strain damage model. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Castañar, Inocencio – PersonEntity: Name: NameFull: Codina, Ramon – PersonEntity: Name: NameFull: Baiges, Joan IsPartOfRelationships: – BibEntity: Dates: – D: 15 M: 06 Text: Jun2026 Type: published Y: 2026 Identifiers: – Type: issn-print Value: 00457825 Numbering: – Type: volume Value: 455 Titles: – TitleFull: Computer Methods in Applied Mechanics & Engineering Type: main |
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