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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]
  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.
Ostien, Jakob T., Foulk, J. W., Mota, A., & Veilleux, M. G. A 10-node composite tetrahedral finite element for solid mechanics. United States. doi:10.1002/nme.5218.
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. doi:10.1002/nme.5218. https://www.osti.gov/servlets/purl/1512889.
@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 = {2016},
month = {2}
}

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Cited by: 11 works
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