Investigation of the nonlinear hyper-viscoelastic behavior of elastomers at finite strain: implementation and numerical validation

Rubber-like materials are known for their time-dependent behavior. The ability to model the hyperviscoelastic behavior of a diverse range of these materials including polymers, elastomers and rubbers is of increasing importance especially in the context of soft tissue mechanics. In this paper, a vis...

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Vydané v:	European physical journal plus Ročník 137; číslo 5; s. 536
Hlavní autori:	Tayeb, Adel, Arfaoui, Makrem, Zine, Abdelmalek, Ichchou, Mohamed, Hamdi, Adel, Ben Abdallah, Jalel
Médium:	Journal Article
Jazyk:	English
Vydavateľské údaje:	Berlin/Heidelberg Springer Berlin Heidelberg 01.05.2022 Springer Nature B.V Springer
Predmet:	Acoustics Algorithms Analysis of PDEs Applied and Technical Physics Atomic Biological clocks Biomechanical engineering Biomechanics Boundary value problems Complex Systems Condensed Matter Physics Constitutive equations Constitutive relationships Decomposition Deformation Elastomers Engineering Sciences Finite element method Functional Analysis Materials Mathematical and Computational Physics Mathematical models Mathematics Molecular Numerical Analysis Optical and Plasma Physics Physics Physics and Astronomy Polymers Reactive fluid environment Regular Article Soft tissues Software Strain Tangent modulus Theoretical Thermodynamics Viscoelasticity
ISSN:	2190-5444, 2190-5444
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Abstract	Rubber-like materials are known for their time-dependent behavior. The ability to model the hyperviscoelastic behavior of a diverse range of these materials including polymers, elastomers and rubbers is of increasing importance especially in the context of soft tissue mechanics. In this paper, a viscohyperelastic model, recently published, is recalled. The implementation of this hyperviscoelastic model at finite strain into the finite element software Abaqus via a umat subroutine is presented. To this end, the discrete form of the constitutive equations of the stress and the tangent modulus following the Jaumann derivative were determined. Then, the implementation was validated using homogeneous tests of simple extension and simple shear for several history of strain and non-homogeneous test of pure torsion of a hollow cylinder. The semi-analytic resolution of the boundary value problems of each test compared to the results of simulation of the implemented model shows a total validation of the implementation algorithm. The implemented model can, therefore, be used in real engineering and biomechanical applications dealing with hyperviscoelastic models.
AbstractList	Rubber-like materials are known for their time-dependent behavior. The ability to model the hyperviscoelastic behavior of a diverse range of these materials including polymers, elastomers and rubbers is of increasing importance especially in the context of soft tissue mechanics. In this paper, a viscohyperelastic model, recently published, is recalled. The implementation of this hyperviscoelastic model at finite strain into the finite element software Abaqus via a umat subroutine is presented. To this end, the discrete form of the constitutive equations of the stress and the tangent modulus following the Jaumann derivative were determined. Then, the implementation was validated using homogeneous tests of simple extension and simple shear for several history of strain and non-homogeneous test of pure torsion of a hollow cylinder. The semi-analytic resolution of the boundary value problems of each test compared to the results of simulation of the implemented model shows a total validation of the implementation algorithm. The implemented model can, therefore, be used in real engineering and biomechanical applications dealing with hyperviscoelastic models.
ArticleNumber	536
Author	Tayeb, Adel Zine, Abdelmalek Ichchou, Mohamed Hamdi, Adel Ben Abdallah, Jalel Arfaoui, Makrem
Author_xml	– sequence: 1 givenname: Adel orcidid: 0000-0003-4136-8779 surname: Tayeb fullname: Tayeb, Adel email: teyebadel@yahoo.fr organization: École Nationale d’Ingénieurs de Tunis, LR-11-ES19 Laboratoire de Mécanique Appliquée et Ingénierie, Université de Tunis El Manar, Laboratoire de tribologie et dynamique des systèmes, Université de Lyon – sequence: 2 givenname: Makrem surname: Arfaoui fullname: Arfaoui, Makrem organization: École Nationale d’Ingénieurs de Tunis, LR-11-ES19 Laboratoire de Mécanique Appliquée et Ingénierie, Université de Tunis El Manar – sequence: 3 givenname: Abdelmalek surname: Zine fullname: Zine, Abdelmalek organization: Institut Camille Jordan, Université de Lyon – sequence: 4 givenname: Mohamed surname: Ichchou fullname: Ichchou, Mohamed organization: Laboratoire de tribologie et dynamique des systèmes, Université de Lyon – sequence: 5 givenname: Adel surname: Hamdi fullname: Hamdi, Adel organization: École Nationale d’Ingénieurs de Tunis, LR-11-ES19 Laboratoire de Mécanique Appliquée et Ingénierie, Université de Tunis El Manar – sequence: 6 givenname: Jalel surname: Ben Abdallah fullname: Ben Abdallah, Jalel organization: École Nationale d’Ingénieurs de Tunis, LR-11-ES19 Laboratoire de Mécanique Appliquée et Ingénierie, Université de Tunis El Manar
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Snippet	Rubber-like materials are known for their time-dependent behavior. The ability to model the hyperviscoelastic behavior of a diverse range of these materials...
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SubjectTerms	Acoustics Algorithms Analysis of PDEs Applied and Technical Physics Atomic Biological clocks Biomechanical engineering Biomechanics Boundary value problems Complex Systems Condensed Matter Physics Constitutive equations Constitutive relationships Decomposition Deformation Elastomers Engineering Sciences Finite element method Functional Analysis Materials Mathematical and Computational Physics Mathematical models Mathematics Molecular Numerical Analysis Optical and Plasma Physics Physics Physics and Astronomy Polymers Reactive fluid environment Regular Article Soft tissues Software Strain Tangent modulus Theoretical Thermodynamics Viscoelasticity
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Title	Investigation of the nonlinear hyper-viscoelastic behavior of elastomers at finite strain: implementation and numerical validation
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