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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Main Authors: Barbora Hálková, Michal Beneš
Format: Article
Language:English
Published: Czech Technical University in Prague 2024-11-01
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.
format Article
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institution DOAJ
issn 2336-5382
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publishDate 2024-11-01
publisher Czech Technical University in Prague
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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