Hyperinelasticity: An energy-based constitutive modelling approach to isothermal large inelastic deformation of polymers. Part I

Abstract

The foundation of a new concept, coined here as hyperinelasticity, is presented in this work for modelling the isothermal elastic and inelastic behaviours of polymers. This concept is based on the premise that both the elastic and inelastic behaviours of the subject specimen in the primary loading path may be characterised by a single constitutive law derived from a comprehensive deformation energy $W$, akin to hyperelasticity, whose constitutive parameters determine and capture both the elastic and inelastic behaviours without the need for additional flow/yield/damage parameters. This core hyperinelastic model captures the elastic and inelastic behaviours in the primary loading path. It is then further specialised, by augmenting the embedded constitutive parameters in the core model, for capturing the inelasticity of the unloading behaviour and the rate of deformation effects. The former is done by devising and incorporating a discontinuous inelasticity variable into the core function, and the latter is achieved by considering that the core model parameters can evolve with, i.e., be a function of, the deformation rate. Examples of the application of the core and augmented hyperinelastic models to a wide range of extant experimental datasets will be presented, ranging from foams, glassy and semi-crystalline polymers to hydrogels and liquid crystal elastomers. The loading modes encompass both tensile and compressive deformations. With a reduced set of number of model parameters (compared with the existing models in the literature), simplicity of implementation (as essentially a straightforward extension to hyperelasticity), and encouraging accuracy in the modelling results, the concept of hyperinelasticity together with the presented hyperinelastic model are proposed as a unified modelling means for capturing the elastic and inelastic behaviours of polymers.