A dynamic variational multiscale method for viscoelasticity using linear tetrahedral elements


Journal Article

Copyright © 2017 John Wiley & Sons, Ltd. 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.

Full Text

Duke Authors

Cited Authors

  • Zeng, X; Scovazzi, G; Abboud, N; Colomés, O; Rossi, S

Published Date

  • December 28, 2017

Published In

Volume / Issue

  • 112 / 13

Start / End Page

  • 1951 - 2003

Electronic International Standard Serial Number (EISSN)

  • 1097-0207

International Standard Serial Number (ISSN)

  • 0029-5981

Digital Object Identifier (DOI)

  • 10.1002/nme.5591

Citation Source

  • Scopus