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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 · · International Journal for Numerical Methods in Engineering
DOI:https://doi.org/10.1002/nme.5138· OSTI ID:1341405
 [1];  [2];  [1];  [1]
  1. Duke Univ., Durham, NC (United States)
  2. 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.
Research Organization:
Sandia National Laboratories (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, Journal Name: International Journal for Numerical Methods in Engineering Journal Issue: 10 Vol. 106; ISSN 0029-5981
Publisher:
WileyCopyright Statement
Country of Publication:
United States
Language:
English

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Cited By (12)

A first-order hyperbolic framework for large strain computational solid dynamics: An upwind cell centred Total Lagrangian scheme: A CELL CENTRED FINITE VOLUME METHOD FOR LARGE STRAIN SOLID DYNAMICS
  • Haider, Jibran; Lee, Chun Hean; Gil, Antonio J.
  • International Journal for Numerical Methods in Engineering, Vol. 109, Issue 3 https://doi.org/10.1002/nme.5293
journal August 2016
Modification of the quadratic 10-node tetrahedron for thin structures and stiff materials under large-strain hyperelastic deformation: Modification of 10-node tetrahedron for large-strain deformation journal January 2018
Elastoplasticity with linear tetrahedral elements: A variational multiscale method: Linear and finite elastoplasticity with tetrahedral elements journal May 2018
Novel quadratic Bézier triangular and tetrahedral elements using existing mesh generators: Applications to linear nearly incompressible elastostatics and implicit and explicit elastodynamics: Novel Bézier elements for nearly incompressible linear elasticity journal October 2018
Novel quadratic Bézier triangular and tetrahedral elements using existing mesh generators: Extension to nearly incompressible implicit and explicit elastodynamics in finite strains journal March 2019
An energy‐stable mixed formulation for isogeometric analysis of incompressible hyperelastodynamics journal July 2019
Numerical recipes for elastodynamic virtual element methods with explicit time integration
  • Park, Kyoungsoo; Chi, Heng; Paulino, Glaucio H.
  • International Journal for Numerical Methods in Engineering, Vol. 121, Issue 1 https://doi.org/10.1002/nme.6173
journal October 2019
Versatile stabilized finite element formulations for nearly and fully incompressible solid mechanics journal September 2019
A Concept of Cell-Based Smoothed Finite Element Method Using 10-Node Tetrahedral Elements (CS-FEM-T10) for Large Deformation Problems of Nearly Incompressible Solids journal October 2019
A conservative penalisation strategy for the semi-implicit time discretisation of the incompressible elastodynamics equation journal December 2018
An energy-stable mixed formulation for isogeometric analysis of incompressible hyper-elastodynamics text January 2018
Versatile stabilized finite element formulations for nearly and fully incompressible solid mechanics text January 2019

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