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

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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.

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Data Availability Statement

This manuscript has associated data in a data repository. [Authors’ comment: The Umat subroutine used in this work can be found in the appendix of the PhD thesis: Contribution to the modelling of the viscoelastic behavior of elastomers with Payne effect, url: http://www.theses.fr/2017LYSEC062.]

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Acknowledgements

This work is part of the ENIT/ECL/ArianeGroup Project that is financially supported by ArianeGroup. We thank sincerely all the associated partners for the realization of this work, in particular Bernard Troclet and Stephane Muller from ArianeGroup.

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  1. École Nationale d’Ingénieurs de Tunis, LR-11-ES19 Laboratoire de Mécanique Appliquée et Ingénierie, Université de Tunis El Manar, Rue Béchir Salem Belkhiria Campus universitaire, BP 37, 1002, Tunis, Tunisia

    Adel Tayeb, Makrem Arfaoui, Adel Hamdi & Jalel Ben Abdallah

  2. Laboratoire de tribologie et dynamique des systèmes, Université de Lyon, 36 Avenue Guy de Collongue, Ecully, 69130, Lyon, France

    Adel Tayeb & Mohamed Ichchou

  3. Institut Camille Jordan, Université de Lyon, 36 Avenue Guy de Collongue, Ecully, 69130, Lyon, France

    Abdelmalek Zine

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  1. Adel Tayeb
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Tayeb, A., Arfaoui, M., Zine, A. et al. Investigation of the nonlinear hyper-viscoelastic behavior of elastomers at finite strain: implementation and numerical validation. Eur. Phys. J. Plus 137, 536 (2022). https://doi.org/10.1140/epjp/s13360-022-02757-w

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