Modified Yeoh model with improved equibiaxial loading predictions

Abstract

Based on two sets of experimental data from the literature, one for vulcanized rubber and the other for a thermoplastic elastomer, the Yeoh model was found to underestimate the stress during equibiaxial loading. The Biderman model, whose strain energy density function expression differs from that of the Yeoh model by an additional term containing the second invariant, overestimates the stress in the mentioned loading mode leading to severe inaccuracies. For improved predictions, this work proposes the modification of the Yeoh model in which the residual strain energy density from equibiaxial loading is fitted to a term with dependence on the second invariant and thereafter adding the term to the original expression. The model constants and predictions were obtained by implementing the Levenberg–Marquardt algorithm and the Cauchy stress tensor equations, respectively, in Python codes. Both the coefficient of determination and the relative errors were utilized to quantify the accuracy of the model predictions. The modified model exhibited superior predictive capabilities particularly in equibiaxial loading where it reduced the average relative error from 22.07 to 6.09 and 27.25 to 10.39% for vulcanized rubber and thermoplastic elastomer data, respectively. For complete behavior, i.e., the average of the relative errors in the three loading modes, the modified version's value was half that of the Yeoh model. This demonstrated its suitability for predicting the multi-axial loading behavior of elastomer-based engineering components.