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Pathologies associated with the numerical analysis of hyper‐anisotropic materials
Author(s) -
šimáček Pavel,
Kaliakin Victor N.,
Pipes R. Byron
Publication year - 1993
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.1620362006
Subject(s) - spurious relationship , compressibility , eigenvalues and eigenvectors , kinematics , anisotropy , constraint (computer aided design) , finite element method , numerical analysis , simple (philosophy) , mathematics , mathematical analysis , structural engineering , mechanics , materials science , geometry , physics , classical mechanics , engineering , optics , statistics , philosophy , epistemology , quantum mechanics
The rise in popularity of composite materials has brought to light the necessity of analysing materials exhibiting the kinematic constraint of directional inextensibility. Numerical phenomena associated with the analysis of such hyperanisotropic materials are described herein. The phenomena include: element locking dependent on fibre orientation, spurious tension modes and difficulties associated with elements possessing large material parameter ratios. To facilitate the present description, these phenomena are compared to, and contrasted with the well‐documented problems associated with the analysis of incompressible or nearly incompressible media. Based on the results of eigenvalue analyses, elements satisfying the Babuška‐Brezzi condition for incompressible media are found to perform rather poorly when analysing hyperanisotropic materials. These findings are supported by the results of a simple example.