A dynamic variational multiscale method for viscoelasticity using linear tetrahedral elements

Xianyi Zeng, Guglielmo Scovazzi*, Nabil Abboud, Oriol Colomés, Simone Rossi

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

27 Citations (Scopus)


In this article, we develop a dynamic version of the variational multiscale (D-VMS) stabilization for nearly/fully incompressible solid dynamics simulations of viscoelastic materials. The constitutive models considered here are based on Prony series expansions, which are rather common in the practice of finite element simulations, especially in industrial/commercial applications. Our method is based on a mixed formulation, in which the momentum equation is complemented by a pressure equation in rate form. The unknown pressure, displacement, and velocity are approximated with piecewise linear, continuous finite element functions. To prevent spurious oscillations, the pressure equation is augmented with a stabilization operator specifically designed for viscoelastic problems, in that it depends on the viscoelastic dissipation. We demonstrate the robustness, stability, and accuracy properties of the proposed method with extensive numerical tests in the case of linear and finite deformations.

Original languageEnglish
Pages (from-to)1951-2003
Number of pages53
JournalInternational Journal for Numerical Methods in Engineering
Issue number13
Publication statusPublished - 28 Dec 2017
Externally publishedYes


  • piece-wise linear interpolation
  • stabilized methods
  • tetrahedral finite element
  • transient dynamics
  • viscoelasticity


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