Modelling the finite deformation of thermoplastic polymers via hyperinelasticity. Part I: A semi-crystalline polymer under varying crystallinity ratios and deformation rates

The aim of this two-part paper series is to present the application of a new modelling approach, namely hyperinelasticity, to the large elastic and inelastic deformation behaviours of thermoplastic polymers. In this first contribution, namely Part I, we are concerned with modelling the large deformation of semi-crystalline polymers, by way of considering Polyethylene (PE) specimens. The deformation behaviour of PE samples under uniaxial tensile deformation with various crystallinity ratios and under different deformation rates is modelled. A core deformation energy function $W$ will be utilised, as a function of the first $\left(I_1\right)$ and second $\left(I_2\right)$ principal invariants of the Cauchy–Green deformation tensor(s). This core function will then be augmented to incorporate the additional inelasticity-inducing factors of crystallinity ratio and the rate of deformation. The general theoretical framework for this incorporation is underpinned, and specific appropriate measures of those inelasticity-inducing factors will be defined and devised, incorporated into the core model. The ensuing augmented model is then fitted with the experimental data, showing favourable affinity and modelling results. Using the calibrated model, predictions of the large deformations of the specimens at other ratios/rates will also be made, and verified against the experimental data. The simplicity of the model, its amenability for incorporating additional inelastic effects, and its ability in providing both accurate simulations and predictions of the elastic and inelastic behaviours of the samples concludes its versatility and usefulness for application to the finite strains of semi-crystalline polymers. Part II will investigate and present the specialised application of the same modelling approach to the elastic and inelastic behaviours of amorphous polymers.