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Failures of the three‐dimensional patch test for large elastic deformations
Author(s) -
Jabareen M.,
Rubin M. B.
Publication year - 2010
Publication title -
international journal for numerical methods in biomedical engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.741
H-Index - 63
eISSN - 2040-7947
pISSN - 2040-7939
DOI - 10.1002/cnm.1248
Subject(s) - structural engineering , context (archaeology) , bending , nonlinear system , eigenvalues and eigenvectors , tension (geology) , finite element method , stiffness , stiffness matrix , compression (physics) , hourglass , anisotropy , mathematical analysis , materials science , mechanics , engineering , physics , mathematics , composite material , geology , paleontology , quantum mechanics , astronomy
Within the context of 3‐D brick elements for nonlinear elastic materials it is well know that enhanced strain and incompatible mode methods can be used successfully to improve the accuracy of solutions for bending of thin structures. It is also known that these elements can exhibit unphysical hourglass instabilities in states of combined high compression and bending. Here, examples of large deformation uniaxial strain in tension indicate that the enhanced strain/incompatible mode elements in ABAQUS, ADINA and ANSYS predict negative eigenvalues in the stiffness matrix which can cause failure of the three‐dimensional patch test. Specifically, the elements in ABAQUS and ANSYS predict unstable element response with multiple unphysical solutions for a constant value of stretch. In contrast, the Cosserat point element (CPE) analytically satisfies the three‐dimensional patch test for all anisotropic nonlinear elastic materials and all reference element shapes. Copyright © 2009 John Wiley & Sons, Ltd.