Application of fractional calculus methods to viscoelastic behaviours of solid propellants

Abstract

<jats:p>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.</jats:p> <jats:p>This article is part of the theme issue ‘Advanced materials modelling via fractional calculus: challenges and perspectives'.</jats:p>

Advanced materials modelling via fractional calculus: challenges and perspectives

“…The work is complemented by a critical discussion on further potential applications of the model as well as on its limitations. Fang et al [52] propose a threebranch fractional-derivative viscoelastic model for solid propellants. The model provides a good agreement with experimental data in terms of stress relaxation modulus and storage modulus, using a limited number of parameters compared with traditional models containing integer-order derivatives; the study is complemented by a simple and effective direct search method for data fitting.…”

“…The theme issue includes several contributions on linear and nonlinear fractional viscoelasticity, as applied to various types of materials [50][51][52][53][54][55]. Atanackovic et al [50] investigate the thermo-dynamical restrictions on constitutive equations for viscoelastic fluids, as following from a weak form of entropy inequality under isothermal conditions.…”

Existence Results for a Multipoint Fractional Boundary Value Problem in the Fractional Derivative Banach Space

“…It is noticeable, in recent years, that the field of fractional calculus has been swept for research by many mathematicians, due to its effectiveness in describing many physical phenomena, see, e.g., [1][2][3][4][5][6][7].…”

Theoretical Analysis of Fractional Viscoelastic Flow in Circular Pipes: General Solutions

“…The comprehensive overview summarizing state-of-the-art practical applications of FC has been recently published by The Royal Society Publishing. The sixteen-paper issue entitled "Advanced materials modeling via fractional calculus: challenges and perspectives" [12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27] covers applications of constant-order (CO) and variable-order (VO) fractional differential operators to several fundamental phenomena. These include anomalous diffusion, [13,16] heat conduction [14,27], fractional viscoelasticity of fluids [19], and materials [12,18,22].…”

“…The sixteen-paper issue entitled "Advanced materials modeling via fractional calculus: challenges and perspectives" [12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27] covers applications of constant-order (CO) and variable-order (VO) fractional differential operators to several fundamental phenomena. These include anomalous diffusion, [13,16] heat conduction [14,27], fractional viscoelasticity of fluids [19], and materials [12,18,22]. The approach to model viscoelastic properties of materials with VO FC operators is undoubtedly among the most promising ones, as it allows for the consideration of fractional order dynamics with respect to time, space, and material variables [22].…”