Encyclopedia of Continuum Mechanics

Living Edition
| Editors: Holm Altenbach, Andreas Öchsner

Fractal Viscoelastic Models

  • Wen ChenEmail author
  • Wei Cai
  • Hongguang Sun
  • Yingjie Liang
Living reference work entry
DOI: https://doi.org/10.1007/978-3-662-53605-6_78-1



Introduction of the Hausdorff derivative, a new kind of methodology, for modeling viscoelastic behaviors.


Viscoelastic Behaviors of Materials

A wide range of materials, such as rubber, soft soil, blood, colloid, and polymer in the real world, are observed to simultaneously exhibit both the elastic and viscous behaviors. It is well known that the stress, respectively, in purely elastic and viscous process is linear to the strain and the rate of strain. In contrast, the viscoelastic stress response of viscoelastic materials is dependent on time and strain rate, leading to complex behaviors of creep and relaxation in the case of certain stress or constraint. Such power-law responses are usually considered as memorial behaviors, in other words, history-dependent process.

In addition, some viscoelastic materials present certain abnormal properties in the frequency domain, such as frequency-dependent damping and energy...

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  • Wen Chen
    • 1
    Email author
  • Wei Cai
    • 2
  • Hongguang Sun
    • 1
  • Yingjie Liang
    • 1
  1. 1.State Key Laboratory of Hydrology-Water Resources and Hydraulic Engineering, Institute of Soft Matter Mechanics, College of Mechanics and MaterialsHohai UniversityNanjingChina
  2. 2.College of Mechanical and Electrical EngineeringHohai UniversityChangzhouChina

Section editors and affiliations

  • Yury A. Rossikhin (deceased)
    • 1
  • Marina V. Shitikova
    • 2
  1. 1.Research Center on Dynamics of Solids and StructuresVoronezh State Technical UniversityVoronezhRussia
  2. 2.Research Center on Dynamics of Solids and StructuresVoronezh State Technical UniversityVoronezhRussia