Fractional order models of viscoelastic polymeric solids undergoing large deformations
We present a fractional order model for nonlinear visco-hyperelastic solids taking into account large deformations. A three-field form of the Hu-Washizu principle is introduced to create a stable finite element method in the context of nearly incompressible dynamics. The β-method (a generalized mid...
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| Format: | Article |
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Czech Technical University in Prague
2024-11-01
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| Series: | Acta Polytechnica CTU Proceedings |
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| Online Access: | https://ojs.cvut.cz/ojs/index.php/APP/article/view/10202 |
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| author | Barbora Hálková Michal Beneš |
| author_facet | Barbora Hálková Michal Beneš |
| author_sort | Barbora Hálková |
| collection | DOAJ |
| description |
We present a fractional order model for nonlinear visco-hyperelastic solids taking into account large deformations. A three-field form of the Hu-Washizu principle is introduced to create a stable finite element method in the context of nearly incompressible dynamics. The β-method (a generalized midpoint rule) for time discretization is implemented into a variational finite element framework for efficient computing of numerical approximations to the initial boundary-value problem for hyperbolic equation of motion. Finally, a 2-D cantilever beam problem with a step end load is considered in order to demonstrate the algorithm.
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| format | Article |
| id | doaj-art-954f575bc80b4dee84025be6b89bbb3a |
| institution | DOAJ |
| issn | 2336-5382 |
| language | English |
| publishDate | 2024-11-01 |
| publisher | Czech Technical University in Prague |
| record_format | Article |
| series | Acta Polytechnica CTU Proceedings |
| spelling | doaj-art-954f575bc80b4dee84025be6b89bbb3a2025-08-20T02:52:31ZengCzech Technical University in PragueActa Polytechnica CTU Proceedings2336-53822024-11-014910.14311/APP.2024.49.0013Fractional order models of viscoelastic polymeric solids undergoing large deformationsBarbora Hálková0Michal Beneš1Czech Technical University in Prague, Faculty of Civil Engineering, Department of Mechanics, Thákurova 7, 166 29 Prague, Czech RepublicCzech Technical University in Prague, Faculty of Civil Engineering, Department of Mathematics, Thákurova 7, 166 29 Prague, Czech Republic We present a fractional order model for nonlinear visco-hyperelastic solids taking into account large deformations. A three-field form of the Hu-Washizu principle is introduced to create a stable finite element method in the context of nearly incompressible dynamics. The β-method (a generalized midpoint rule) for time discretization is implemented into a variational finite element framework for efficient computing of numerical approximations to the initial boundary-value problem for hyperbolic equation of motion. Finally, a 2-D cantilever beam problem with a step end load is considered in order to demonstrate the algorithm. https://ojs.cvut.cz/ojs/index.php/APP/article/view/10202fractional viscoelasticitylarge deformationsspringpotfractional calculusfinite elementintegration algorithm |
| spellingShingle | Barbora Hálková Michal Beneš Fractional order models of viscoelastic polymeric solids undergoing large deformations Acta Polytechnica CTU Proceedings fractional viscoelasticity large deformations springpot fractional calculus finite element integration algorithm |
| title | Fractional order models of viscoelastic polymeric solids undergoing large deformations |
| title_full | Fractional order models of viscoelastic polymeric solids undergoing large deformations |
| title_fullStr | Fractional order models of viscoelastic polymeric solids undergoing large deformations |
| title_full_unstemmed | Fractional order models of viscoelastic polymeric solids undergoing large deformations |
| title_short | Fractional order models of viscoelastic polymeric solids undergoing large deformations |
| title_sort | fractional order models of viscoelastic polymeric solids undergoing large deformations |
| topic | fractional viscoelasticity large deformations springpot fractional calculus finite element integration algorithm |
| url | https://ojs.cvut.cz/ojs/index.php/APP/article/view/10202 |
| work_keys_str_mv | AT barborahalkova fractionalordermodelsofviscoelasticpolymericsolidsundergoinglargedeformations AT michalbenes fractionalordermodelsofviscoelasticpolymericsolidsundergoinglargedeformations |