A 10‐node composite tetrahedral finite element for solid mechanics

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 o...

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Bibliographic Details
Published in:International journal for numerical methods in engineering 2016-09, Vol.107 (13), p.1145-1170
Main Authors: Ostien, J. T., Foulk, J. W., Mota, A., Veilleux, M. G.
Format: Article
Language:English
Subjects:
Deformation effects
ENGINEERING
Exact solutions
Finite element method
Hu‐Washizu
MATERIALS SCIENCE
Mathematical analysis
mixed formulation
Plasticity
Representations
Solid mechanics
tetrahedron
Variational principles
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Summary: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.
ISSN:0029-5981
1097-0207
DOI:10.1002/nme.5218