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Stress–displacement stabilized finite element analysis of thin structures using Solid-Shell elements, Part II: Finite strain hyperelasticity.

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Title: Stress–displacement stabilized finite element analysis of thin structures using Solid-Shell elements, Part II: Finite strain hyperelasticity.
Authors: Aguirre, A.1,2 (AUTHOR) alejandro.aguirre@upc.edu, Codina, R.1,3 (AUTHOR) ramon.codina@upc.edu, Baiges, J.1,3 (AUTHOR) joan.baiges@upc.edu, Castañar, I.1 (AUTHOR) icastanar@cimne.upc.edu
Source: Finite Elements in Analysis & Design. Sep2024, Vol. 236, pN.PAG-N.PAG. 1p.
Subjects: Finite element method, Displacement (Mechanics), Hypergraphs, Infinitesimal geometry
Abstract: This work is the second of a two-part research project focused on modeling solid-shell elements using a stabilized two-field finite element formulation. The first part introduces a stabilization technique based on the Variational Multiscale framework, which is proven to effectively address numerical locking in infinitesimal strain problems. The primary objective of the study was to characterize the inherent numerical locking effects of solid-shell elements in order to comprehensively understand their triggers and how stabilized mixed formulations can overcome them. In this current phase of the work, the concept is extended to finite strain solid dynamics involving hyperelastic materials. The aim of introducing this method is to obtain a robust stabilized mixed formulation that enhances the accuracy of the stress field. This improved formulation holds great potential for accurately approximating shell structures undergoing finite deformations. To this end, three techniques based in the Variational Multiscale stabilization framework are presented. These stabilized formulations allow circumventing the compatibility restriction of interpolating spaces of the unknowns inherent to mixed formulations, thus allowing any combination of them. The accuracy of the stress field is successfully enhanced while maintaining the accuracy of the displacement field. These improvements are also inherited to the solid-shell elements, providing locking-free approximation of thin structures. • A Stabilized finite element method for the mixed displacement–stress approach is presented. • Solid-shell models are considered in finite strain hyperelasticity using the total Lagrangian approach. • The fully stabilized and linearized formulation is presented. • The final formulation is accurate and robust, free of any type of locking. [ABSTRACT FROM AUTHOR]
Copyright of Finite Elements in Analysis & Design 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
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Header DbId: egs
DbLabel: Engineering Source
An: 177420114
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PubType: Academic Journal
PubTypeId: academicJournal
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  Data: Stress–displacement stabilized finite element analysis of thin structures using Solid-Shell elements, Part II: Finite strain hyperelasticity.
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  Data: <searchLink fieldCode="JN" term="%22Finite+Elements+in+Analysis+%26+Design%22">Finite Elements in Analysis & Design</searchLink>. Sep2024, Vol. 236, pN.PAG-N.PAG. 1p.
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  Data: <searchLink fieldCode="DE" term="%22Finite+element+method%22">Finite element method</searchLink><br /><searchLink fieldCode="DE" term="%22Displacement+%28Mechanics%29%22">Displacement (Mechanics)</searchLink><br /><searchLink fieldCode="DE" term="%22Hypergraphs%22">Hypergraphs</searchLink><br /><searchLink fieldCode="DE" term="%22Infinitesimal+geometry%22">Infinitesimal geometry</searchLink>
– Name: Abstract
  Label: Abstract
  Group: Ab
  Data: This work is the second of a two-part research project focused on modeling solid-shell elements using a stabilized two-field finite element formulation. The first part introduces a stabilization technique based on the Variational Multiscale framework, which is proven to effectively address numerical locking in infinitesimal strain problems. The primary objective of the study was to characterize the inherent numerical locking effects of solid-shell elements in order to comprehensively understand their triggers and how stabilized mixed formulations can overcome them. In this current phase of the work, the concept is extended to finite strain solid dynamics involving hyperelastic materials. The aim of introducing this method is to obtain a robust stabilized mixed formulation that enhances the accuracy of the stress field. This improved formulation holds great potential for accurately approximating shell structures undergoing finite deformations. To this end, three techniques based in the Variational Multiscale stabilization framework are presented. These stabilized formulations allow circumventing the compatibility restriction of interpolating spaces of the unknowns inherent to mixed formulations, thus allowing any combination of them. The accuracy of the stress field is successfully enhanced while maintaining the accuracy of the displacement field. These improvements are also inherited to the solid-shell elements, providing locking-free approximation of thin structures. • A Stabilized finite element method for the mixed displacement–stress approach is presented. • Solid-shell models are considered in finite strain hyperelasticity using the total Lagrangian approach. • The fully stabilized and linearized formulation is presented. • The final formulation is accurate and robust, free of any type of locking. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of Finite Elements in Analysis & Design 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:
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        Value: 10.1016/j.finel.2024.104179
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      – Code: eng
        Text: English
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        PageCount: 1
        StartPage: N.PAG
    Subjects:
      – SubjectFull: Finite element method
        Type: general
      – SubjectFull: Displacement (Mechanics)
        Type: general
      – SubjectFull: Hypergraphs
        Type: general
      – SubjectFull: Infinitesimal geometry
        Type: general
    Titles:
      – TitleFull: Stress–displacement stabilized finite element analysis of thin structures using Solid-Shell elements, Part II: Finite strain hyperelasticity.
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            NameFull: Aguirre, A.
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            NameFull: Codina, R.
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            NameFull: Baiges, J.
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            NameFull: Castañar, I.
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            – D: 01
              M: 09
              Text: Sep2024
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              Y: 2024
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              Value: 236
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