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A dynamic variational multiscale method for viscoelasticity using linear tetrahedral elements

Publication ,  Journal Article
Zeng, X; Scovazzi, G; Abboud, N; Colomés, O; Rossi, S
Published in: International Journal for Numerical Methods in Engineering
December 28, 2017

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.

Duke Scholars

Published In

International Journal for Numerical Methods in Engineering

DOI

EISSN

1097-0207

ISSN

0029-5981

Publication Date

December 28, 2017

Volume

112

Issue

13

Start / End Page

1951 / 2003

Related Subject Headings

  • Applied Mathematics
  • 40 Engineering
  • 09 Engineering
 

Citation

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Zeng, X., Scovazzi, G., Abboud, N., Colomés, O., & Rossi, S. (2017). A dynamic variational multiscale method for viscoelasticity using linear tetrahedral elements. International Journal for Numerical Methods in Engineering, 112(13), 1951–2003. https://doi.org/10.1002/nme.5591
Zeng, X., G. Scovazzi, N. Abboud, O. Colomés, and S. Rossi. “A dynamic variational multiscale method for viscoelasticity using linear tetrahedral elements.” International Journal for Numerical Methods in Engineering 112, no. 13 (December 28, 2017): 1951–2003. https://doi.org/10.1002/nme.5591.
Zeng X, Scovazzi G, Abboud N, Colomés O, Rossi S. A dynamic variational multiscale method for viscoelasticity using linear tetrahedral elements. International Journal for Numerical Methods in Engineering. 2017 Dec 28;112(13):1951–2003.
Zeng, X., et al. “A dynamic variational multiscale method for viscoelasticity using linear tetrahedral elements.” International Journal for Numerical Methods in Engineering, vol. 112, no. 13, Dec. 2017, pp. 1951–2003. Scopus, doi:10.1002/nme.5591.
Zeng X, Scovazzi G, Abboud N, Colomés O, Rossi S. A dynamic variational multiscale method for viscoelasticity using linear tetrahedral elements. International Journal for Numerical Methods in Engineering. 2017 Dec 28;112(13):1951–2003.
Journal cover image

Published In

International Journal for Numerical Methods in Engineering

DOI

EISSN

1097-0207

ISSN

0029-5981

Publication Date

December 28, 2017

Volume

112

Issue

13

Start / End Page

1951 / 2003

Related Subject Headings

  • Applied Mathematics
  • 40 Engineering
  • 09 Engineering