Acta Mechanica Sinica

, Volume 17, Issue 4, pp 354–365

# FE formulation for the viscoelastic body modeled by fractional constitutive law

• Zhang Wei
• Nobuyuki Shimizu
Article

## Abstract

This paper presents finite element (FE) formulation of the viscoelastic materials described by fractional constitutive law. The time-domain three-dimensional constitutive equation is constructed. The FE equations are set up by equations are solved by numerical integration method. The numerical algorithm developed by the authors for Liouville-Riemann's fractional derivative was adopted to formulate FE procedures and extended to solve the more general case of the hereditary integration. The numerical examples were given to show the correctness and effectiveness of the integration algorithm.

### Key Words

viscoelasticity fractional calculus FEM polymer materials

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## Copyright information

© Chinese Society of Theoretical and Applied Mechanics 2001

## Authors and Affiliations

• Zhang Wei
• 1
• Nobuyuki Shimizu
• 2
1. 1.Institute of Applied MechanicsJinan UniversityGuangzhouChina
2. 2.Department of Mechanical EngineeringIwaki Meisei UniversityJapan