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

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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.

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Acknowledgements

We would like to thank the colleagues of the “Laboratoire d’Hydraulique et de l’Environnement” of the University of Bejaia, Route de Targua Ouzrmmour, Bejaia, Algeria to have allowed us to use FE Comsol Multiphysics code.

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  1. Laboratoire de Mécanique, Matériaux & Énergétique (L2ME), Faculté de Technologie, Université de Bejaia, 06000, Bejaia, Algeria

    Kamel Yaya & Hocine Bechir

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  1. Kamel Yaya
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  2. Hocine Bechir
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Correspondence to Kamel Yaya.

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Yaya, K., Bechir, H. A new hyper-elastic model for predicting multi-axial behaviour of rubber-like materials: formulation and computational aspects. Mech Time-Depend Mater 22, 167–186 (2018). https://doi.org/10.1007/s11043-017-9355-y

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