Variable-order fractional description of compression deformation of amorphous glassy polymers

  • Ruifan Meng
  • Deshun YinEmail author
  • Corina S. Drapaca
Original Paper


In this paper, the variable order fractional constitutive model is adopted to describe the compression deformation of amorphous glassy polymers. In order to keep the fractional order within the definition of viscoelasticity, a three-regions- fitting-method is proposed. By using this, the value of fractional order is found to be a constant in viscoelastic region, and decreases linearly in both strain softening and strain hardening regions. The corresponding mechanical property evolution revealed by fractional order is proved to be reasonable based on the molecular chains conflict theory. And a comparison study is conducted to show the advantage of using the variable order fractional model with higher accuracy and fewer parameters. It is then concluded that the variable order fractional calculus is an efficient tool to predict the compression deformation of amorphous glassy polymers.


Variable order fractional calculus Amorphous glassy polymers Compression Mechanical property Molecular chains 



This work is supported by the Chinese Scholarship Council (No. 201606710068) and “the Fundamental Research Funds for the Central Universities” (No. 2016B44914), for which we are very grateful.


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

Authors and Affiliations

  1. 1.College of Mechanics and MaterialsHohai UniversityNanjingPeople’s Republic of China
  2. 2.Department of Engineering Science and MechanicsThe Pennsylvania State UniversityUniversity ParkUSA

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