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A 10‐node composite tetrahedral finite element for solid mechanics
Author(s) -
Ostien J. T.,
Foulk J. W.,
Mota A.,
Veilleux M. G.
Publication year - 2016
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.5218
Subject(s) - finite element method , tetrahedron , isochoric process , hyperelastic material , mathematics , context (archaeology) , element (criminal law) , mixed finite element method , extended finite element method , smoothed finite element method , mathematical analysis , geometry , structural engineering , boundary knot method , physics , engineering , boundary element method , paleontology , biology , political science , law , thermodynamics
Summary We propose 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 demonstrated by hyperelastic and inelastic calculations. Copyright © 2016 John Wiley & Sons, Ltd.