Eight-chain and full-network models and their modified versions for rubber hyperelasticity: a comparative study

Abstract

The eight-chain model, also known as ArrudaBoyce model, is widely used to capture the rate-independent hyperelastic response of rubber-like materials. The parameters of this model are physically based and explained from micromechanics of chain molecules. Despite its excellent performance with only two material parameters to capture bench measurements in uniaxial and pure shear regime, the model is known to be significantly deficient in predicting the equibiaxial data. To ameliorate such drawback, over the years, several modified versions of this successful model have been proposed in the literature. The so-called full-network model is another micromechanically motivated chain model, which has also few modified versions in the literature. For this study, two modified versions of the full-network model have been selected. In this contribution, five modified versions of the Arruda-Boyce model and two modified versions of full-network model are critically compared with the classical eight-chain model for their adequacy in representing equibiaxial data. To do a comparison of all selected models in reproducing the well-known Treloar data, the analytical expressions for the three homogeneous deformation modes, that is, uniaxial tension, equibiaxial tension, and pure shear have been derived and the performances of the selected models are analysed. The comparative study demonstrates that modified Flory-Erman model, Gornet-Desmorat (GD) model, Meissner-Matějka model, and bootstrapped eight-chain model predict well the three deformation modes compare to the classical eight-chain model.

Addition of Graphite Filler to Enhance Electrical, Morphological, Thermal, and Mechanical Properties in Poly (Ethylene Terephthalate): Experimental Characterization and Material Modeling

“…To predict the behavior of unfilled polymers, at first we take energy functions of two widely-used classical models, i.e., neo-Hooke (NH) and Carrol (C) models as ΨNH=sans-serifμ2(I1−3),ΨnormalC=aI1+bI14+cI2 where sans-serifμ,a,b,c are material parameters of respective models that need to be identified from appropriate sets of experimental data (see Steinmann et al [63]). Note that there are two modeling approaches for polymers discussed in the literature [63,64,65,66]: (i) micro-mechanically motivated models; and (ii) phenomenological-motivated models. The neo-Hookean model we used initially has both the micro-mechanical and phenomenological explanations [34,66,67].…”

“…For detailed derivations of Equation (9), readers may consult the works of Steinmann et al [63], Hossain et al [64,65,68], and Liao et al [69]. To predict the behavior of filled polymers at large strains, Mullins and Tobin [70] introduced the notion of so-called amplified stretch Λ, which in the case of a uniaxial loading, is related to the actual axial stretch λ by Λ=1+X(λ−1) where X is the stretch amplification factor that depends on the fraction of filler vf.…”

Modelling electro-active polymers with a dispersion-type anisotropy

“…Other advanced forms of energy functions for rubber-like materials can be coupled with the electric part of the energy to improve the modelling, cf. [32,33,62]. A Neo-Hookean coupled isotropic free energy function is thus…”

On thermo-viscoelastic experimental characterization and numerical modelling of VHB polymer

“…Each stress mentioned above requires a separate energy function to have a complete representation. For the ground state elasticity, the Carrol [10] model is chosen since it has shown excellent performance in fitting hyperelastic experimental data of polymeric materials with only three material parameters, see Steinmann et al [56], Hossain et al [18,19,21]. Hence, a Carrol-type energy function is…”