New constitutive models for the finite deformation of isotropic compressible elastomers

Afshin Anssari-Benam, Cornelius O. Horgan

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The application of a new family of strain energy functions to modelling the finite deformation of isotropic compressible elastomers, including polymeric foams and (hydro)gels, is presented in this paper. The proposed family of models is developed from a parent incompressible strain energy function, customised to the compressible case via an additive split of deviatoric and volumetric contributions. With a minimum of four and maximum of five parameters, the developed models are shown to be compatible with the empirical deformation kinematics of slight compressibility (or almost incompressibility) and provide favourable fits to the extant deformation datasets by simultaneous fitting to uniaxial, biaxial and/or simple shear deformations. Some intricate behaviours such as the shear-softening of polystyrene foams and the ensuing instability under simple shearing, as well as the simple tension of alginate-based hydrogels under extremely high levels of stretch are also successfully modelled. Given the versatility of the proposed family of models in terms of their relatively low number of model parameters, their capability to predict a wide range of deformation behaviours for a wide range of elastomers (from foams to gels), and the robustness of the provided fits, the advantages of the considered models over the existing models of the same class in the literature is demonstrated.
Original languageEnglish
JournalMechanics of Materials
Early online date15 Jun 2022
Publication statusEarly online - 15 Jun 2022


  • Polymeric foams
  • Hydrogels
  • Compressibility
  • Finite deformation
  • Modelling
  • Strain energy function


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