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On transformations and shape functions for enhanced assumed strain elements
Author(s) -
Pfefferkorn Robin,
Betsch Peter
Publication year - 2019
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.6133
Subject(s) - curvilinear coordinates , transformation (genetics) , nonlinear system , element (criminal law) , field (mathematics) , mathematics , frame (networking) , computer science , algorithm , topology (electrical circuits) , geometry , pure mathematics , physics , telecommunications , biochemistry , chemistry , quantum mechanics , political science , law , gene , combinatorics
Summary We summarize several previously published geometrically nonlinear EAS elements and compare their behavior. Various transformations for the compatible and enhanced deformation gradient are examined. Their effect on the patch test is one main concern of the work, and it is shown numerically and with a novel analytic proof that the improved EAS element proposed by Simo et al in 1993 does not fulfill the patch test. We propose a modification to overcome that drawback without losing the favorable locking‐free behavior of that element. Furthermore, a new transformation for the enhanced field is proposed and motivated in a curvilinear coordinate frame. It is shown in numerical tests that this novel approach outperforms all previously introduced transformations.