A pseudo-hyperelastic model incorporating the rate effects for isotropic rubber-like materials

Afshin Anssari-Benam, Mokarram Hossain

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An alternative modelling framework is proposed for capturing the rate-dependency in the loading and unloading (i.e., with softening) deformation behaviour of a wide range of isotropic incompressible elastomers. The proposed framework departs from the existing approaches in the literature which assume an additive contribution of the ‘non-equilibrium’, or ‘viscous’, part to the elastic response. Instead, here it is considered that the model parameters of the basic hyperelastic function evolve (i.e., vary) with the deformation rate. That is, the basic hyperelastic model parameters are considered as functions of rate, given the deformation rate as a parameter and not a variable, pre-set in experiments. While the nature, and choice, of this functional dependency is empirical, a simple linear relationship is considered in this work between the parameters of a chosen basic hyperelastic model and the applied deformation rate. Using this specialisation, the model is applied to extant experimental data of a variety of elastomers including 3D-printed elastomeric polyurethane (EPU), dielectric elastomer VHB 4910, commercial 3D-printed silicone (SIL30) and filled rubber Viton™ specimens under uniaxial loading – unloading deformations at various rates. It is shown that the model favourably captures the considered datasets. The mathematical simplicity of the proposed modelling framework, comparatively lower number of model parameters, and the favourable modelling and predictive results suggest that the implementation and application of this modelling framework is efficient and tractable, and merit further consideration for modelling the rate-dependant mechanical behaviour of a wider range of rubber-like materials and loading modalities.
Original languageEnglish
Article number105347
Pages (from-to)1-20
Number of pages10
JournalJournal of the Mechanics and Physics of Solids
Early online date19 Jul 2023
Publication statusPublished - 1 Oct 2023


  • rate-dependency
  • elastomers
  • constitutive modelling
  • softening
  • rate of deformation

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