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Stabilized four‐node tetrahedron with nonlocal pressure for modeling hyperelastic materials
Author(s) -
Areias P.,
Matouš K.
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.2357
Subject(s) - hyperelastic material , finite element method , spurious relationship , helmholtz free energy , linearization , tetrahedron , quantum nonlocality , node (physics) , mathematics , mathematical analysis , classical mechanics , physics , nonlinear system , geometry , thermodynamics , statistics , quantum mechanics , quantum entanglement , quantum
Non‐linear hyperelastic response of reinforced elastomers is modeled using a novel three‐dimensional mixed finite element method with a nonlocal pressure field. The element is unconditionally convergent and free of spurious pressure modes. Nonlocal pressure is obtained by an implicit gradient technique and obeys the Helmholtz equation. Physical motivation for this nonlocality is shown. An implicit finite element scheme with consistent linearization is presented. Finally, several hyperelastic examples are solved to demonstrate the computational algorithm including the inf–sup and verifications tests. Copyright © 2008 John Wiley & Sons, Ltd.