Anisotropic finite strain viscoelasticity: Constitutive modeling and finite element implementation

Hongliang Liu, Gerhard A. Holzapfel, Bjørn H. Skallerud, Victorien Prot*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


A new anisotropic finite strain viscoelastic model is presented, which is based on the Holzapfel type anisotropic hyperelastic strain-energy function. The anisotropic viscous part is set to be independent from the isotropic viscous part. A corresponding multiplicative decomposition of the deformation gradient is presented, and a specific definition of the anisotropic viscous fiber term. A new method to develop the evolution equations of the viscous internal variables is also provided. The time derivatives of the internal variables for the isotropic and anisotropic viscous parts are obtained from the evolution equation of the second Piola–Kirchhoff stress for the viscous part. The corresponding analytical validation of non-negative dissipation using the second law of thermodynamics is provided. The incompressible plane stress case is used to achieve an analytical solution for the proposed constitutive model. A good agreement between the finite element results and the analytical solution is obtained. Finally, some numerical simulations are presented, including the viscous hysteresis response, experimental data fitting and a relaxation test.

Original languageEnglish
Pages (from-to)172-188
Number of pages17
JournalJournal of the Mechanics and Physics of Solids
Publication statusPublished - 1 Mar 2019


  • Anisotropic viscoelasticity
  • Finite strain
  • Internal variable
  • Numerical simulation
  • Relaxation test

ASJC Scopus subject areas

  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering


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