Strain Rate-Dependent Nonlinear Fractional Order Modeling of Elastomer Polymers: A Comprehensive Power-Law Approach
Abstract
To exactly and comprehensively characterise the stress-strain evolution of elastomer polymers, a continuous power-law variable fractional order constitutive model with full correlation of strain rates is proposed in this study. Firstly, the influence weights of each parameter in the order model on the stress-strain mechanical curve are analyzed, and it is found that the variable order is most affected by the strain rate. Further, the order model between the variable order fraction and the strain rate is compared and discussed in different strain rate ranges, and the strain rate-dependent continuous power-law order model is determined. Then, based on the equivalent criterion of strain rate and relaxation time, the power function relationships between the elastic modulus and relaxation time and the derivative of strain rate are established, thus the fractional order constitutive model is integrated and established. Subsequently, the applicability and accuracy of the strain rate fully correlated fractional constitutive model are verified by using the test data in strain rates of 0.0001s-1~9000s-1. Compared with the existing variable fractional constitutive model, the proposed model has higher accuracy (the RMSE is reduced by 4.77 times, the prediction error is less than 0.05%) and faster calculation, and realizes the strain rate sensitivity prediction of material mechanical properties.