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

Research articles | 更新时间：2026-07-24

- Fractional calculus-based modeling of constitutive relations for viscoelastic materials
- Acta Scientiarum Naturalium Universitatis Sunyatseni Vol. 65, Issue 4, Pages: 94-104(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：13 May 2026，
  
  Published：25 July 2026
- 稿件说明：
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王滢淳,刘济科,蔡盛名等.基于分数阶微积分的黏弹性材料本构关系建模[J].中山大学学报(自然科学版)(中英文),2026,65(04):94-104.

Wang Yingchun,Liu Jike,Cai Shengming,et al.Fractional calculus-based modeling of constitutive relations for viscoelastic materials[J].Acta Scientiarum Naturalium Universitatis Sunyatseni,2026,65(04):94-104.
王滢淳,刘济科,蔡盛名等.基于分数阶微积分的黏弹性材料本构关系建模[J].中山大学学报(自然科学版)(中英文),2026,65(04):94-104. DOI： 10.11714/acta.snus.ZR20260053.

Wang Yingchun,Liu Jike,Cai Shengming,et al.Fractional calculus-based modeling of constitutive relations for viscoelastic materials[J].Acta Scientiarum Naturalium Universitatis Sunyatseni,2026,65(04):94-104. 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

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