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Extending a 10‐node composite tetrahedral finite element for solid mechanics
Author(s) -
Foulk III James W.,
Ostien Jakob T.,
Talamini Brandon,
Tupek Michael R.,
Crane Nathan K.,
Mota Alejandro,
Veilleux Michael G.
Publication year - 2021
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.6684
Subject(s) - tetrahedron , finite element method , jacobian matrix and determinant , mathematics , gaussian integral , mathematical analysis , gaussian quadrature , quadratic equation , mixed finite element method , geometry , physics , nyström method , thermodynamics , integral equation
We propose to extend the composite tetrahedral finite element first introduced by Thoutireddy et al. (2002) and recently reformulated by Ostien et al. (2016). We generalize the gradient operator and mass matrix to curved domains through analytical expressions weighted by subtetrahedra Jacobians. Optimal integration weights are constructed to increase the accuracy of Gaussian quadrature. We preserve the variational structure of the formulation through a new five‐field functional with additional, independent fields for the Jacobian and the pressure. This approach not only obviates volumetric locking but also yields symmetry. A deleterious soft mode, common to both the quadratic and composite tetrahedral element with constant pressure formulations is effectively stabilized through a novel convex energy penalty function. Numerous numerical examples spanning a patch test to the impact of a Taylor bar demonstrate the accuracy, robustness, and convergence of the extended composite tetrahedral element for application to structural metals.