A simple, stable, and accurate linear tetrahedral finite element for transient, nearly, and fully incompressible solid dynamics: A dynamic variational multiscale approach [A simple, stable, and accurate tetrahedral finite element for transient, nearly incompressible, linear and nonlinear elasticity: A dynamic variational multiscale approach]

Scovazzi, Guglielmo; Carnes, Brian; Zeng, Xianyi; Rossi, Simone

doi:10.1002/nme.5138

Title: A simple, stable, and accurate linear tetrahedral finite element for transient, nearly, and fully incompressible solid dynamics: A dynamic variational multiscale approach [A simple, stable, and accurate tetrahedral finite element for transient, nearly incompressible, linear and nonlinear elasticity: A dynamic variational multiscale approach]

Journal Article · Thu Nov 12 00:00:00 EST 2015 · International Journal for Numerical Methods in Engineering

DOI:https://doi.org/10.1002/nme.5138· OSTI ID:1341405

Scovazzi, Guglielmo ^[1]; Carnes, Brian ^[2]; Zeng, Xianyi ^[1]; Rossi, Simone ^[1]

Duke Univ., Durham, NC (United States)
Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)

Here, we propose a new approach for the stabilization of linear tetrahedral finite elements in the case of nearly incompressible transient solid dynamics computations. Our method is based on a mixed formulation, in which the momentum equation is complemented by a rate equation for the evolution of the pressure field, approximated with piece-wise linear, continuous finite element functions. The pressure equation is stabilized to prevent spurious pressure oscillations in computations. Incidentally, it is also shown that many stabilized methods previously developed for the static case do not generalize easily to transient dynamics. Extensive tests in the context of linear and nonlinear elasticity are used to corroborate the claim that the proposed method is robust, stable, and accurate.

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Research Organization:: Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)

Sponsoring Organization:: USDOE National Nuclear Security Administration (NNSA)

Grant/Contract Number:: AC04-94AL85000

OSTI ID:: 1341405

Report Number(s):: SAND-2016-12567J; 649881

Journal Information:: International Journal for Numerical Methods in Engineering, Vol. 106, Issue 10; ISSN 0029-5981

Publisher:: WileyCopyright Statement

Country of Publication:: United States

Language:: English

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Cited by: 75 works

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