Fractional calculus-based modeling of constitutive relations for viscoelastic materials

Wang Yingchun; Liu Jike; Cai Shengming; Chen Yanmao; Liu Qixian

doi:10.11714/acta.snus.ZR20260053

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Fractional calculus-based modeling of constitutive relations for viscoelastic materials

更新时间：2026-05-15

- Fractional calculus-based modeling of constitutive relations for viscoelastic materials
- Acta Scientiarum Naturalium Universitatis Sunyatseni Pages: 1-11(2026)
- 作者机构：
  
  中山大学航空航天学院，广东深圳 518107
- 作者简介：
- 基金信息：
- DOI：10.11714/acta.snus.ZR20260053
  CLC： O34
- Received：03 March 2026，
  
  Accepted：07 April 2026，
  
  Online First：15 May 2026，
- 稿件说明：
移动端阅览
Wang Yingchun, Liu Jike, Cai Shengming, et al. Fractional calculus-based modeling of constitutive relations for viscoelastic materials[J/OL]. Acta Scientiarum Naturalium Universitatis Sunyatseni, 2026, 1-11.
DOI：

Wang Yingchun, Liu Jike, Cai Shengming, et al. Fractional calculus-based modeling of constitutive relations for viscoelastic materials[J/OL]. Acta Scientiarum Naturalium Universitatis Sunyatseni, 2026, 1-11. DOI： 10.11714/acta.snus.ZR20260053.

摘要

基于分数阶黏弹性力学理论和经典元件，建立了可精确表征高聚物蠕变及动态力学行为的本构模型。针对材料流变过程中的损伤演化特性，引入考虑时间效应的损伤变量，构建含损伤分数阶本构关系，有效表征材料在应力松弛、加速蠕变等复杂非线性过程中的力学响应。为验证模型可靠性，基于分数阶 Poynting-Thomson 模型搭建动态力学分析模型，并通过动态力学实验开展对比验证。结果表明，模型拟合的迟滞环曲线与试验数据吻合度高，证明了分数阶导数在高聚物黏弹性动态力学性能描述中的有效性。

Abstract

Based on the theory of fractional-order viscoelastic mechanics and classical elements， a constitutive model has been established that can accurately characterize the creep and dynamic mechanical behavior of polymers. In response to the damage evolution characteristics during the material rheological process， a damage variable considering time effects is introduced to construct a damage-involved fractional-order constitutive relationship， effectively representing the mechanical response of the material in complex nonlinear processes such as stress relaxation and accelerated creep. To verify the reliability of the model， a dynamic mechanical analysis model was built based on the fractional-order Poynting-Thomson model， and comparative validation was conducted through dynamic mechanical experiments. The results show that the hysteresis loop curves fitted by the model are highly consistent with the experimental data， demonstrating the effectiveness of fractional derivatives in describing the dynamic mechanical properties of polymers.

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references

李列列，管俊峰，肖明砾，等， 2020 . 一种横观各向同性岩体蠕变模型［J］. 岩土力学， 41 （ 9 ）： 2922 - 2930+2942 .

汪洋，陈建康，李克武，等， 2017蠕变条件下刚性夹杂填充高聚物复合材料的延迟时间-蠕变荷载幂率关系研究［J］. 固体力学学报， 38 （ 4 ）： 348 - 358 .

王玉娇， 2014 . 分数阶导数及其应用［D］. 太原：太原理工大学 .

Bagley R L ， Torvik P J ， 1983 . A theoretical basis for the application of fractional Calculus to viscoelasticity ［J］. J Rheol ， 27 （ 3 ）： 201 - 210 .

Ding P ， Xu R ， Zhu Y ， et al ， 2022 . Correction to：Fractional derivative modelling for rheological consolidation of multilayered soil under time-dependent loadings and continuous permeable boundary conditions ［J］. Acta Geotech ， 17 （ 8 ）： 3695 .

Esmaeeli R ， Farhad S ， 2020 . Parameters estimation of generalized Maxwell model for SBR and carbon-filled SBR using a direct high-frequency DMA measurement system ［J］. Mech Mater ， 146 ： 103369 .

Göbel L ， Flohr A ， Osburg A ， et al ， 2025 . Deciphering the contribution of polymer latexes on the viscoelastic behavior of hardened cement pastes by means of dynamic-mechanical analysis ［J］. Case Stud Constr Mater ， 22 ： e04460 .

Li X ， Shao H ， 2024 . Investigation of bio-thermo-mechanical responses based on nonlocal elasticity theory and fractional Pennes equation ［J］. Appl Math Model ， 125 ： 390 - 401 .

Meng R ， Cao L ， Zhang Q ， 2023 . Study on the performance of variable-order fractional viscoelastic models to the order function parameters ［J］. Appl Math Model ， 121 ： 430 - 444 .

Pierro E ， Carbone G ， 2021 . A new technique for the characterization of viscoelastic materials：Theory，experiments and comparison with DMA ［J］. J Sound Vib ， 515 ： 116462 .

Popov V L ， Heß M ， Willert E ， 2019 . Viscoelastic materials ［M］// Handbook of Contact Mechanics . Berlin， Heidelberg ： Springer： 213 - 249 .

Rahman G U ， Ahmad D ， GóMez-Aguilar J F ， et al ， 2025 . Study of Caputo fractional derivative and Riemann-Liouville integral with different orders and its application in multi-term differential equations ［J］. Math Meth Appl Sci ， 48 （ 2 ）： 1464 - 1502 .

Sun W ， Yuan Y X ， 2006 . Optimization theory and methods ［M］. New York ： Springer： 71- 117 .

Tayyebati M ， Sarhadi A ， Fraisse A ， et al ， 2025 . Effects of high-cycle fatigue on the viscoelastic properties of epoxy resin ［J］. Eur J Mech A ， 112 ： 105641 .

Vishnukumar K S ， Vellappandi M ， Govindaraj V ， 2024 . Reachability of time-varying fractional dynamical systems with Riemann-Liouville fractional derivative ［J］. Fract Calc Appl Anal ， 27 （ 3 ）： 1328 - 1347 .

Wang Z ， Liu Y ， Zhang B ， et al ， 2025 . Creep performance and viscoelastic constitutive relationship of structural acrylic connected using bulk polymerization technique ［J］. Buildings ， 15 （ 20 ）： 3691 .

Xiang G ， Yin D ， Meng R ， et al ， 2021 . Predictive model for stress relaxation behavior of glassy polymers based on variable-order fractional Calculus ［J］. Polym Adv Technol ， 32 （ 2 ）： 703 - 713 .

Ye L T ， Chen Y M ， Liu J K ， et al ， 2026 . Fractional gradient-enhanced generalized response sensitivity approach for parameter identification with applications in fractional-order systems ［J］. Commun Nonlinear Sci Numer Simul ， 152 ： 109349 .

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