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Finite element simulation of the viscoelastic behavior of elastomers under finite deformation with consideration of nonlinear material viscosity

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Abstract

Governed by the diffusion process of the highly mobile and flexible polymer chains, viscoelasticity is one crucial property in modeling the finite deformation of elastomers. While the development of new constitutive models has drawn remarkable attention to reveal the underlying mechanisms of material viscosity, it becomes very challenging to predict the viscoelastic behavior of elastomers, particularly when a complex structure is undergoing non-uniform deformation. The current work attempts to fill this knowledge gap by establishing a finite element (FE) framework to numerically predict the viscoelastic behavior of elastomeric materials. In this FE framework, the micro–macro constitutive model recently proposed by Zhou et al. (J Mech Phys Solids 110:137–154, 2018. https://doi.org/10.1016/j.jmps.2017.09.016), which is capable of capturing the nonlinear viscosity and the microstructure features of the material, is implemented by developing the user-defined material (UMAT) subroutine in the software Abaqus. The developed UMAT is featured by the capability of adopting most of the constitutive relations in terms of either strain invariants or principal stretches, indicating the adaptiveness of the FE framework. The accuracy and the modeling capacity of the FE framework are validated with several numerical examples on three commonly used elastomeric materials, including VHB 4910, HNBR50, and carbon black filled elastomers, under various loading conditions. The comparison of the viscoelastic responses shows an excellent agreement between the FE modeling results and the theoretical analysis. The established FE model is expected to provide guidance for novel design and applications of elastomer-based structures. The framework can also be further extended to characterize the multiphysics coupling behaviors of elastomeric materials under coupled fields.

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Acknowledgements

This work is supported by the Natural Sciences and Engineering Research Council of Canada (NSERC).

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This work is supported by the Natural Sciences and Engineering Research Council of Canada (NSERC).

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  1. Department of Mechanical and Materials Engineering, The University of Western Ontario, London, ON, N6A 5B9, Canada

    Heng Feng, Shan Gao & Liying Jiang

  2. School of Science, Harbin Institute of Technology, Shenzhen, 518055, China

    Jianyou Zhou

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Feng, H., Zhou, J., Gao, S. et al. Finite element simulation of the viscoelastic behavior of elastomers under finite deformation with consideration of nonlinear material viscosity. Acta Mech 232, 4111–4132 (2021). https://doi.org/10.1007/s00707-021-03042-0

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