A new hyper-elastic model for predicting multi-axial behaviour of rubber-like materials: formulation and computational aspects

Abstract

We propose a new hyper-elastic model that is based on the standard invariants of Green–Cauchy. Experimental data reported by Treloar (Trans. Faraday Soc. 40:59, 1944) are used to identify the model parameters. To this end, the data of uni-axial tension and equi-bi-axial tension are used simultaneously. The new model has four material parameters, their identification leads to linear optimisation problem and it is able to predict multi-axial behaviour of rubber-like materials. We show that the response quality of the new model is equivalent to that of the well-known Ogden six parameters model. Thereafter, the new model is implemented in FE code. Then, we investigate the inflation of a rubber balloon with the new model and Ogden models. We compare both the analytic and numerical solutions derived from these models.