New Model for Hyper-Elastic Materials Behavior With an Application on Natural Rubber

Abstract

This paper is concerned with defining a new Weight Function Based model (WFB), which describes the hyper-elastic materials stress-strain behavior. Numerous hyper-elastic theoretical material models have been proposed over the past 60 years capturing the stress-strain behavior of large deformation incompressible isotropic materials. The newly proposed method has been verified against the historic Treloar’s test data for uni-axial, bi-axial and pure shear loadings of Treloar’s vulcanized rubber material, showing a promising level of confidence compared to the Ogden and the Yeoh methods. A non-linear least square optimization Matlab tool was used to determine the WFB, Yeoh and Ogden models material parameters. A comparison between the results of the three models was performed showing that the newly proposed model is more accurate for uni-axial tension as it has an error value which is less than the Ogden and Yeoh models by 1.0 to 39%. Also, the parameters calculation by more than 95%, for the bi-axial and pure shear loading cases compared to the Ogden model. Natural rubber test specimens have been tensioned using a tensile testing machine and the WFB model was applied to fit the test data results showing a very good curve fitting with an average error of 0.44%.WFB model has reduced processing time for the model.