A three-parameter structurally motivated robust constitutive model for isotropic incompressible unfilled and filled rubber-like materials

Abstract

A structurally motivated three-parameter strain energy function W is presented in this paper for application to the constitutive modelling of various types of incompressible isotropic rubber-like materials, from unfilled to filled rubbers, polymers and soft tissues. A particular objective of the current work is to achieve another step towards devising a comprehensive model for application to an assortment of incompressible isotropic hyperelastic materials, not limited only to a specific subset type of rubbers or polymers. To this end, the application of the model to extant datasets from various types of rubber-like materials is presented, via simultaneous fitting of the model to the considered deformation modes. The modelling results are then compared with those of a selected set of established three-parameter models in the literature, including a generalised neo-Hookean strain energy function and another two models which include an I2 term. It will be shown that the proposed model most favourably captures the datasets for all unfilled, filled rubber and polymer specimens considered. Finally, the model is applied to the deformation datasets of a soft tissue, namely the human brain, for which the (one-term) Ogden model is currently known to provide the best fit. It will be demonstrated that the application of the Ogden model will lead to loss of convexity, while our proposed model provides a better fit, with lower relative errors, and remains convex over the deformation domain. By way of the presented examples and applications, it is concluded that the proposed model provides a reliable degree of robustness for a suitable application to constitutive modelling of various types of rubber-like materials.