Improved five-parameter fractional derivative model for elastomers

Abstract

The dynamic behaviour of elastomers is assumed to follow a constitutive differential equation of non-integral (fractional) order. In order to describe the peculiar frequency response of the loss factor, the constitutive equation has been refined by introducing the fifth parameter to the classical fourth-order equation. The asymmetry of the loss factor in the frequency domain comes from the different time-derivative orders of the stress and strain. Either smooth asymmetry or stabilization by a plateau at high frequency can be modelled by suitable difference between the two orders of the time derivatives. The physical validity of the model is discussed and a parametrical analysis is conducted on diagrams relating the height and the width of the loss factor.