A generalisation of the Pucci-Saccomandi model of rubber elasticity

The Pucci-Saccomandi model of rubber elasticity, also known as the Gent-Gent model, is generalised in this manuscript for a more enhanced applicability to a wider range of finite deformation behaviours, rubber-like material types, and an increased modelling accuracy. The generalising of interest is developed by devising a higher order rational approximant, i.e., of order [1/1], of the response functions. The proposed model is shown to be a parent to some of the celebrated limiting chain extensibility, classical.. (I-1, I-2) and generalised neo-Hookean models. The application of the proposed generalised model to the finite deformation of various isotropic incompressible rubber-like materials is demonstrated, including natural unfilled and filled rubbers, commercial polymers and biomaterials. The considered datasets exhibit various deformation behaviours from the classical large deformation of natural rubbers to the downward concavity of filled rubbers, strain/shear softening behaviours of polymers and the softening behaviour of biomaterials up to the onset of failure. The modelling results are directly compared with those of the Gent-Gent model, where the higher accuracy of the proposed model and its capability to favourably capture the aforementioned challenging and varied behaviours is established. In particular, the Gent-Gent model is shown unsuitable for capturing such downward concavity, shear/strain softening and continuous softening to failure behaviours. Given the improved modelling predictions, simplicity of the functional form of the devised model, and its relatively low number of model parameters, the proposed model is presented as a more general, comprehensive and versatile modelling tool for application to the finite deformation of various isotropic incompressible soft materials.