Determination of Suitable Hyper Elastic Material Model through Non-Linear Regression Analysis

Abstract

The material behaviour of elastomers can be simulated through Strain Energy Density (SED) function which can be defined by the following hyper plastic material models: (i) Neo-Hookean, (ii) Mooney-Rivlin, (iii) Yeoh and (iv) Ogden. The stress-strain relations of the above-mentioned SED functions for uni-axial tension, planar (pure shear) tension and equi-biaxial tension are validated with Treloar’s data. Different combinations of Treloar’s data are used to determine the co-efficient of SED functions of the above said models. These co-efficient values are determined using the software like ANSYS, MATLAB and POLYMATH and the validation of the results is carried out based on sum of squared error (SSE) which is calculated between the experimental values and predicted values. From the result, it is found that SSE less than 5 and closer to 0 can be taken as good prediction for selection of material model and co-efficient of material models. The engineering stress-strain behaviour of synthetic rubber (NBR) is obtained experimentally from uni-axial tension test and the co-efficient of SED functions are determined.