Application of fractional calculus methods to viscoelastic behaviours of solid propellants

A three-branch viscoelastic model based on fractional derivatives is proposed for the viscoelastic behaviours of solid propellants. The simulation results show a satisfactory agreement with the stress relaxation modulus and complex modulus of solid propellants. As a comparison, the static modulus is also characterized by traditional viscoelastic model with integer-order derivatives. Results show that the application of the fractional derivatives to the viscoelastic constitutive model can effectively reduce the number of the required parameters while giving an accurate prediction of viscoelastic behaviours of solid propellants. Moreover, a simple and effective direct search method based on simulated annealing and Powell's mothed is proposed for the data fitting. This article is part of the theme issue 'Advanced materials modelling via fractional calculus: challenges and perspectives'.