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Stabilization of mixed tetrahedral elements at large deformations
Author(s) -
Caylak Ismail,
Mahnken Rolf
Publication year - 2011
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.3320
Subject(s) - tetrahedron , finite element method , compressibility , linear elasticity , plasticity , elasticity (physics) , mathematics , discontinuous deformation analysis , deformation (meteorology) , finite strain theory , mathematical analysis , geometry , materials science , structural engineering , mechanics , physics , engineering , composite material
SUMMARY This paper presents stabilized mixed finite element formulations for tetrahedral elements at large deformations using volume and area bubble functions. To this end, the corresponding weak formulations are derived for the standard two‐field method, the method of incompatible modes and the enhanced strain method. Then, the weak formulations will be linearized. Furthermore, the matrix formulations for the weak formulations and its linearizations are summarized. The numerical results for incompressible rubber‐like materials using a Neo‐Hookean material law show the locking‐free performance and the drastic damping of the stresses for the new stabilized tetrahedral elements in finite deformation problems. This paper is an extension of the works published by the authors regarding small deformation problems for linear elasticity and plasticity. Copyright © 2011 John Wiley & Sons, Ltd.