New polynomial strain energy function; application to rubbery circular cylinders under finite extension and torsion

Abstract

ABSTRACTIn this article, a strain energy density function is proposed in terms of the principal invariants of the left Cauchy‐Green strain tensor for Rubber‐like materials. This model due to its mathematical structure lies in the category of polynomial hyperelastic models. To compare the performance of the proposed model with the Rivlin set, some test data of rubber‐like materials with pure homogeneous deformations are used. It is shown that the proposed model has better agreement with the test data compared to the selected model. As an application of the proposed model, it is used to obtain a closed form solution for analysis of rubbery solid circular cylinders with S‐shaped and semi J‐shaped mechanical behavior under the torsion superimposed on the axial extension. Moreover, the results predicted from the proposed model are compared to classic models to investigate the results accuracy for simplification done. © 2014 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2015, 132, 41718.