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A uniform nodal strain tetrahedron with isochoric stabilization
Author(s) -
Gee M. W.,
Dohrmann C. R.,
Key S. W.,
Wall W. A.
Publication year - 2008
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.2493
Subject(s) - isochoric process , tetrahedron , strain energy , infinitesimal strain theory , finite element method , instability , materials science , spurious relationship , deformation (meteorology) , multistability , rigidity (electromagnetism) , geometry , mechanics , mathematics , physics , nonlinear system , thermodynamics , composite material , statistics , quantum mechanics
A stabilized node‐based uniform strain tetrahedral element is presented and analyzed for finite deformation elasticity. The element is based on linear interpolation of a classical displacement‐based tetrahedral element formulation but applies nodal averaging of the deformation gradient to improve mechanical behavior, especially in the regime of near‐incompressibility where classical linear tetrahedral elements perform very poorly. This uniform strain approach adopted here exhibits spurious modes as has been previously reported in the literature. We present a new type of stabilization exploiting the circumstance that the instability in the formulation is related to the isochoric strain energy contribution only and we therefore present a stabilization based on an isochoric–volumetric splitting of the stress tensor. We demonstrate that by stabilizing the isochoric energy contributions only, reintroduction of volumetric locking through the stabilization can be avoided. The isochoric–volumetric splitting can be applied for all types of materials with only minor restrictions and leads to a formulation that demonstrates impressive performance in examples provided. Copyright © 2008 John Wiley & Sons, Ltd.