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Title: A 10-node composite tetrahedral finite element for solid mechanics

Abstract

We present a reformulation of the composite tetrahedral finite element first introduced by Thoutireddy et al. By choosing a different numerical integration scheme, we obtain an element that is more accurate than the one proposed in the original formulation. We also show that in the context of Lagrangian approaches, the gradient and projection operators derived from the element reformulation admit fully analytic expressions, which offer a significant improvement in terms of accuracy and computational expense. For plasticity applications, a mean-dilatation approach on top of the underlying Hu–Washizu variational principle proves effective for the representation of isochoric deformations. The performance of the reformulated element is shown by hyperelastic and inelastic calculations.

Authors:
 [1];  [1];  [1];  [1]
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  1. Sandia National Lab. (SNL-CA), Livermore, CA (United States)
Publication Date:
Research Org.:
Sandia National Lab. (SNL-CA), Livermore, CA (United States)
Sponsoring Org.:
USDOE National Nuclear Security Administration (NNSA)
OSTI Identifier:
1512889
Report Number(s):
SAND-2015-6621J
Journal ID: ISSN 0029-5981; 670404
Grant/Contract Number:  
AC04-94AL85000
Resource Type:
Accepted Manuscript
Journal Name:
International Journal for Numerical Methods in Engineering
Additional Journal Information:
Journal Volume: 107; Journal Issue: 13; Journal ID: ISSN 0029-5981
Publisher:
Wiley
Country of Publication:
United States
Language:
English
Subject:
42 ENGINEERING; 36 MATERIALS SCIENCE; Hu‐Washizu; tetrahedron; mixed formulation; plasticity

Citation Formats

Ostien, Jakob T., Foulk, J. W., Mota, A., and Veilleux, M. G. A 10-node composite tetrahedral finite element for solid mechanics. United States: N. p., 2016. Web. doi:10.1002/nme.5218.
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Ostien, Jakob T., Foulk, J. W., Mota, A., & Veilleux, M. G. A 10-node composite tetrahedral finite element for solid mechanics. United States. https://doi.org/10.1002/nme.5218
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Ostien, Jakob T., Foulk, J. W., Mota, A., and Veilleux, M. G. Sun . "A 10-node composite tetrahedral finite element for solid mechanics". United States. https://doi.org/10.1002/nme.5218. https://www.osti.gov/servlets/purl/1512889.
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@article{osti_1512889,
title = {A 10-node composite tetrahedral finite element for solid mechanics},
author = {Ostien, Jakob T. and Foulk, J. W. and Mota, A. and Veilleux, M. G.},
abstractNote = {We present a reformulation of the composite tetrahedral finite element first introduced by Thoutireddy et al. By choosing a different numerical integration scheme, we obtain an element that is more accurate than the one proposed in the original formulation. We also show that in the context of Lagrangian approaches, the gradient and projection operators derived from the element reformulation admit fully analytic expressions, which offer a significant improvement in terms of accuracy and computational expense. For plasticity applications, a mean-dilatation approach on top of the underlying Hu–Washizu variational principle proves effective for the representation of isochoric deformations. The performance of the reformulated element is shown by hyperelastic and inelastic calculations.},
doi = {10.1002/nme.5218},
journal = {International Journal for Numerical Methods in Engineering},
number = 13,
volume = 107,
place = {United States},
year = {Sun Feb 21 00:00:00 EST 2016},
month = {Sun Feb 21 00:00:00 EST 2016}
}
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Journal Article:
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Publisher's Version of Record
https://doi.org/10.1002/nme.5218
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Citation Metrics:
Cited by: 24 works
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Figures / Tables:

Figure 1 Figure 1: Geometry and node numbering for the composite tetrahedron.
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Works referenced in this record:

A uniform nodal strain tetrahedron with isochoric stabilization
journal, April 2009

  • Gee, M. W.; Dohrmann, C. R.; Key, S. W.
  • International Journal for Numerical Methods in Engineering, Vol. 78, Issue 4
  • DOI: 10.1002/nme.2493

3D Composite Finite Elements for Elliptic Boundary Value Problems with Discontinuous Coefficients
journal, January 2011

  • Preusser, Tobias; Rumpf, Martin; Sauter, Stefan
  • SIAM Journal on Scientific Computing, Vol. 33, Issue 5
  • DOI: 10.1137/100791750

Fifteen node tetrahedral elements for explicit methods in nonlinear solid dynamics
journal, April 2014

Volume conserving finite element simulations of deformable models
journal, July 2007

  • Irving, Geoffrey; Schroeder, Craig; Fedkiw, Ronald
  • ACM Transactions on Graphics, Vol. 26, Issue 3
  • DOI: 10.1145/1276377.1276394

F-bar-based linear triangles and tetrahedra for finite strain analysis of nearly incompressible solids. Part I: formulation and benchmarking
journal, January 2005

  • Neto, E. A. de Souza; Pires, F. M. Andrade; Owen, D. R. J.
  • International Journal for Numerical Methods in Engineering, Vol. 62, Issue 3
  • DOI: 10.1002/nme.1187

Lie-group interpolation and variational recovery for internal variables
journal, June 2013

A stabilized nodally integrated tetrahedral
journal, January 2006

  • Puso, M. A.; Solberg, J.
  • International Journal for Numerical Methods in Engineering, Vol. 67, Issue 6
  • DOI: 10.1002/nme.1651

Tetrahedral composite finite elements
journal, January 2001

  • Thoutireddy, P.; Molinari, J. F.; Repetto, E. A.
  • International Journal for Numerical Methods in Engineering, Vol. 53, Issue 6
  • DOI: 10.1002/nme.337

Triangular composite finite elements
journal, January 2000

Node-based uniform strain elements for three-node triangular and four-node tetrahedral meshes
journal, March 2000

A stabilized mixed finite element method for finite elasticity.
journal, November 1999

  • Klaas, Ottmar; Maniatty, Antoinette; Shephard, Mark S.
  • Computer Methods in Applied Mechanics and Engineering, Vol. 180, Issue 1-2
  • DOI: 10.1016/S0045-7825(99)00059-6

Higher order stabilized finite element method for hyperelastic finite deformation
journal, January 2002

  • Maniatty, Antoinette M.; Liu, Yong; Klaas, Ottmar
  • Computer Methods in Applied Mechanics and Engineering, Vol. 191, Issue 13-14
  • DOI: 10.1016/S0045-7825(01)00335-8

Variational and projection methods for the volume constraint in finite deformation elasto-plasticity
journal, September 1985

  • Simo, J. C.; Taylor, R. L.; Pister, K. S.
  • Computer Methods in Applied Mechanics and Engineering, Vol. 51, Issue 1-3
  • DOI: 10.1016/0045-7825(85)90033-7
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    Works referencing / citing this record:

    Treatment of near-incompressibility in meshfree and immersed-particle methods
    journal, April 2019

    • Moutsanidis, Georgios; Koester, Jacob J.; Tupek, Michael R.
    • Computational Particle Mechanics, Vol. 7, Issue 2
    • DOI: 10.1007/s40571-019-00238-z
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      Figures / Tables found in this record:

      Figure 1 (p. 6)figure
      Table 1 (p. 7)table
      Table 2 (p. 8)table
      Figure 2 (p. 14)figure
      Table 3 (p. 14)table
      Table 4 (p. 15)table
      Figure 3 (p. 16)figure
      Figure 4 (p. 17)figure
      Figure 5 (p. 18)figure
      Figure 6 (p. 19)figure
      Figure 7 (p. 20)figure
      Table 5 (p. 20)table
      Figure 8 (p. 21)figure
      Table 6 (p. 21)table
      Figure 9 (p. 22)figure
      Figure 10 (p. 23)figure
      Figure 11 (p. 24)figure
      Figure 12 (p. 31)figure
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