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]
Abstract
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.
- Authors:
-
- Duke Univ., Durham, NC (United States)
- Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
- Publication Date:
- Research Org.:
- Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
- Sponsoring Org.:
- USDOE National Nuclear Security Administration (NNSA)
- OSTI Identifier:
- 1341405
- Report Number(s):
- SAND-2016-12567J
Journal ID: ISSN 0029-5981; 649881
- Grant/Contract Number:
- AC04-94AL85000
- Resource Type:
- Accepted Manuscript
- Journal Name:
- International Journal for Numerical Methods in Engineering
- Additional Journal Information:
- Journal Volume: 106; Journal Issue: 10; Journal ID: ISSN 0029-5981
- Publisher:
- Wiley
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; tetrahedral finite element; piece-wise linear interpolation; stabilized method; transient dynamics; nearly incompressible elasticity
Citation Formats
Scovazzi, Guglielmo, Carnes, Brian, Zeng, Xianyi, and Rossi, Simone. 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]. United States: N. p., 2015.
Web. doi:10.1002/nme.5138.
Scovazzi, Guglielmo, Carnes, Brian, Zeng, Xianyi, & Rossi, Simone. 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]. United States. https://doi.org/10.1002/nme.5138
Scovazzi, Guglielmo, Carnes, Brian, Zeng, Xianyi, and Rossi, Simone. Thu .
"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]". United States. https://doi.org/10.1002/nme.5138. https://www.osti.gov/servlets/purl/1341405.
@article{osti_1341405,
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]},
author = {Scovazzi, Guglielmo and Carnes, Brian and Zeng, Xianyi and Rossi, Simone},
abstractNote = {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.},
doi = {10.1002/nme.5138},
journal = {International Journal for Numerical Methods in Engineering},
number = 10,
volume = 106,
place = {United States},
year = {Thu Nov 12 00:00:00 EST 2015},
month = {Thu Nov 12 00:00:00 EST 2015}
}
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An energy-stable mixed formulation for isogeometric analysis of incompressible hyper-elastodynamics
text, January 2018
- Liu, Ju; Marsden, Alison L.; Tao, Zhen
- arXiv
Versatile stabilized finite element formulations for nearly and fully incompressible solid mechanics
text, January 2019
- Karabelas, Elias; Haase, Gundolf; Plank, Gernot
- arXiv