A generalised neo-Hookean strain energy function for application to the finite deformation of elastomers

Abstract

We present a new model within the class of generalised neo-Hookean strain energy functions for application to the finite deformation of incompressible elastomers. The model has a simple form with only two parameters, namely μ and N with structural roots, and is derived within the classical framework of statistical mechanics for freely jointed molecular chains in rubber elasticity Using existing experimental datasets of uniaxial, biaxial, and pure shear deformations, including Treloar’s canonical data, we show that the proposed model captures the deformation behaviours of each elastomer specimen with a single set of μ and N values (with only a narrow variation range). We conduct qualitative and quantitative comparative analyses to highlight the advantages of the proposed model, and demonstrate improved fits versus the celebrated Gent model. Given its structural molecular basis, simplicity, small number of parameters, and its capability to describe many deformation modes of a specimen using a single set of parameter values, we propose this model for application to finite deformation of elastomers.