Two viscoelastic constitutive models of rubber materials using fractional derivations

The fractional derivative model,which contains the standard mechanical model,can accurately describe visco-elastic behavior of materials.Frequency sweeping tests are conducted at different temperatures and different strain amplitudes for rubber material to determine the storage modulus,loss modulus and the loss factor at different frequencies.A fractional Kelvin-Voigt model and a higher-order fractional derivative FVMP(fraction Voigt and Maxwell mode in parallel) model are used to predict the frequency response of the material.The results show that the FVMP model better describes the dynamic constitutive relation of the rubber material for various temperatures and strain amplitudes and that there are errors in the fractional Kelvin-Voigt model.