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A variational multiscale method with linear tetrahedral elements for multiplicative viscoelasticity

Publication ,  Journal Article
Abboud, N; Scovazzi, G
Published in: Mechanics Research Communications
March 1, 2021

We present a computational approach to solve problems in multiplicative nonlinear viscoelasticity using piecewise linear finite elements on triangular and tetrahedral grids, which are very versatile for simulations in complex geometry. Our strategy is based on (1) formulating the equations of mechanics as a mixed first-order system, in which a rate form of the pressure equation is utilized in place of the standard constitutive relationship, and (2) utilizing the variational multiscale approach, in which the stabilization parameter is scaled with the viscous energy dissipation.

Duke Scholars

Published In

Mechanics Research Communications

DOI

ISSN

0093-6413

Publication Date

March 1, 2021

Volume

112

Related Subject Headings

  • Mechanical Engineering & Transports
  • 4901 Applied mathematics
  • 4017 Mechanical engineering
  • 4005 Civil engineering
  • 0913 Mechanical Engineering
  • 0905 Civil Engineering
  • 0102 Applied Mathematics
 

Citation

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Abboud, N., & Scovazzi, G. (2021). A variational multiscale method with linear tetrahedral elements for multiplicative viscoelasticity. Mechanics Research Communications, 112. https://doi.org/10.1016/j.mechrescom.2020.103610
Abboud, N., and G. Scovazzi. “A variational multiscale method with linear tetrahedral elements for multiplicative viscoelasticity.” Mechanics Research Communications 112 (March 1, 2021). https://doi.org/10.1016/j.mechrescom.2020.103610.
Abboud N, Scovazzi G. A variational multiscale method with linear tetrahedral elements for multiplicative viscoelasticity. Mechanics Research Communications. 2021 Mar 1;112.
Abboud, N., and G. Scovazzi. “A variational multiscale method with linear tetrahedral elements for multiplicative viscoelasticity.” Mechanics Research Communications, vol. 112, Mar. 2021. Scopus, doi:10.1016/j.mechrescom.2020.103610.
Abboud N, Scovazzi G. A variational multiscale method with linear tetrahedral elements for multiplicative viscoelasticity. Mechanics Research Communications. 2021 Mar 1;112.
Journal cover image

Published In

Mechanics Research Communications

DOI

ISSN

0093-6413

Publication Date

March 1, 2021

Volume

112

Related Subject Headings

  • Mechanical Engineering & Transports
  • 4901 Applied mathematics
  • 4017 Mechanical engineering
  • 4005 Civil engineering
  • 0913 Mechanical Engineering
  • 0905 Civil Engineering
  • 0102 Applied Mathematics