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Numerical Simulations of Three-Dimensional Nonlinear Elasticity Using an Ultraweak Formulation and Polyhedral Finite Elements.

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Title: Numerical Simulations of Three-Dimensional Nonlinear Elasticity Using an Ultraweak Formulation and Polyhedral Finite Elements.
Authors: Mora-Paz, Jaime1 jaimed.morap@konradlorenz.edu.co, Demkowicz, Leszek1 leszek@oden.utexas.edu
Source: Computing in Science & Engineering. Jan-Mar2026, Vol. 28 Issue 1, p52-63. 12p.
Subjects: Computer simulation, Polyhedral functions, Finite element method, Mathematical models, Semantics (Philosophy)
Abstract: We present the derivation and discretization of a novel ultraweak variational formulation for nonlinear elasticity. Moreover, we rely on the ability of polyhedral finite elements (FEs) to capture large deformations of rubber-like materials. For an application example in which an elastomeric foam is subject to large compressive deformations, we run numerical experiments with three FE methods: Bubnov-Galerkin with the classical weak formulation and tetrahedral elements, discontinuous Petrov-Galerkin with the ultraweak formulation and tetrahedral elements, and discontinuous Petrov-Galerkin with the ultraweak formulation and polyhedral elements (PolyDPG). The results for this example show a clear superiority of PolyDPG against the other two methods, having reached a remarkable 52% deformation against 4% and 2.4% reached by the other two. [ABSTRACT FROM AUTHOR]
Copyright of Computing in Science & Engineering is the property of IEEE 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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  Data: Numerical Simulations of Three-Dimensional Nonlinear Elasticity Using an Ultraweak Formulation and Polyhedral Finite Elements.
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  Data: <searchLink fieldCode="JN" term="%22Computing+in+Science+%26+Engineering%22">Computing in Science & Engineering</searchLink>. Jan-Mar2026, Vol. 28 Issue 1, p52-63. 12p.
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  Data: We present the derivation and discretization of a novel ultraweak variational formulation for nonlinear elasticity. Moreover, we rely on the ability of polyhedral finite elements (FEs) to capture large deformations of rubber-like materials. For an application example in which an elastomeric foam is subject to large compressive deformations, we run numerical experiments with three FE methods: Bubnov-Galerkin with the classical weak formulation and tetrahedral elements, discontinuous Petrov-Galerkin with the ultraweak formulation and tetrahedral elements, and discontinuous Petrov-Galerkin with the ultraweak formulation and polyhedral elements (PolyDPG). The results for this example show a clear superiority of PolyDPG against the other two methods, having reached a remarkable 52% deformation against 4% and 2.4% reached by the other two. [ABSTRACT FROM AUTHOR]
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  Data: <i>Copyright of Computing in Science & Engineering is the property of IEEE 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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        Value: 10.1109/MCSE.2025.3635482
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      – Code: eng
        Text: English
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        PageCount: 12
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      – SubjectFull: Polyhedral functions
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      – SubjectFull: Finite element method
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              Text: Jan-Mar2026
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              Y: 2026
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