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Port-Hamiltonian formulation and structure-preserving discretization of finite elasticity based on a mixed Hu-Washizu-type formulation.

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Title: Port-Hamiltonian formulation and structure-preserving discretization of finite elasticity based on a mixed Hu-Washizu-type formulation.
Authors: Hille, Moritz1 (AUTHOR), Betsch, Peter1 (AUTHOR) peter.betsch@kit.edu, Franke, Marlon1 (AUTHOR)
Source: Computer Methods in Applied Mechanics & Engineering. Aug2026, Vol. 458, pN.PAG-N.PAG. 1p.
Subjects: Elasticity, Discretization methods, Numerical analysis, Energy function, Finite element method, Conservation of energy
Abstract: We propose a port-Hamiltonian formulation and structure-preserving discretization of finite elasticity. The energy functional (or Hamiltonian) is based on a polyconvex representation of the stored energy and gives rise to three strain-type fields, which play the role of energy variables in the port-Hamiltonian formulation. We show that a Hu-Washizu-type extension of the variational principle of Livens can be used (i) to derive the continuous port-Hamiltonian formulation and (ii) to perform a structure-preserving spatial discretization. In particular, we show that the spatial finite element discretization of the underlying mixed formulation yields a discrete port-Hamiltonian system. Moreover, the temporal discretization of the underlying continuous formulation yields a new energy-momentum consistent framework, which accommodates alternative finite element formulations. The new framework, in particular, covers mixed finite elements that have been shown to be well suited for handling quasi-incompressible material behavior. Numerical examples are provided to evaluate the numerical performance and stability of the newly devised energy-momentum schemes. [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.)
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DbLabel: Engineering Source
An: 194001899
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  Data: Port-Hamiltonian formulation and structure-preserving discretization of finite elasticity based on a mixed Hu-Washizu-type formulation.
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  Data: <searchLink fieldCode="AR" term="%22Hille%2C+Moritz%22">Hille, Moritz</searchLink><relatesTo>1</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Betsch%2C+Peter%22">Betsch, Peter</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> peter.betsch@kit.edu</i><br /><searchLink fieldCode="AR" term="%22Franke%2C+Marlon%22">Franke, Marlon</searchLink><relatesTo>1</relatesTo> (AUTHOR)
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  Data: <searchLink fieldCode="JN" term="%22Computer+Methods+in+Applied+Mechanics+%26+Engineering%22">Computer Methods in Applied Mechanics & Engineering</searchLink>. Aug2026, Vol. 458, pN.PAG-N.PAG. 1p.
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  Data: <searchLink fieldCode="DE" term="%22Elasticity%22">Elasticity</searchLink><br /><searchLink fieldCode="DE" term="%22Discretization+methods%22">Discretization methods</searchLink><br /><searchLink fieldCode="DE" term="%22Numerical+analysis%22">Numerical analysis</searchLink><br /><searchLink fieldCode="DE" term="%22Energy+function%22">Energy function</searchLink><br /><searchLink fieldCode="DE" term="%22Finite+element+method%22">Finite element method</searchLink><br /><searchLink fieldCode="DE" term="%22Conservation+of+energy%22">Conservation of energy</searchLink>
– Name: Abstract
  Label: Abstract
  Group: Ab
  Data: We propose a port-Hamiltonian formulation and structure-preserving discretization of finite elasticity. The energy functional (or Hamiltonian) is based on a polyconvex representation of the stored energy and gives rise to three strain-type fields, which play the role of energy variables in the port-Hamiltonian formulation. We show that a Hu-Washizu-type extension of the variational principle of Livens can be used (i) to derive the continuous port-Hamiltonian formulation and (ii) to perform a structure-preserving spatial discretization. In particular, we show that the spatial finite element discretization of the underlying mixed formulation yields a discrete port-Hamiltonian system. Moreover, the temporal discretization of the underlying continuous formulation yields a new energy-momentum consistent framework, which accommodates alternative finite element formulations. The new framework, in particular, covers mixed finite elements that have been shown to be well suited for handling quasi-incompressible material behavior. Numerical examples are provided to evaluate the numerical performance and stability of the newly devised energy-momentum schemes. [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:
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      – Type: doi
        Value: 10.1016/j.cma.2026.118790
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      – Code: eng
        Text: English
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        PageCount: 1
        StartPage: N.PAG
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      – SubjectFull: Elasticity
        Type: general
      – SubjectFull: Discretization methods
        Type: general
      – SubjectFull: Numerical analysis
        Type: general
      – SubjectFull: Energy function
        Type: general
      – SubjectFull: Finite element method
        Type: general
      – SubjectFull: Conservation of energy
        Type: general
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      – TitleFull: Port-Hamiltonian formulation and structure-preserving discretization of finite elasticity based on a mixed Hu-Washizu-type formulation.
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            NameFull: Hille, Moritz
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            – D: 15
              M: 08
              Text: Aug2026
              Type: published
              Y: 2026
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              Value: 458
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