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Fast methods for determining instabilities of elastic–plastic damage models through closed‐form expressions
Author(s) -
Xue Liang,
Belytschko Ted
Publication year - 2010
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.2947
Subject(s) - instability , hadamard transform , computation , bifurcation , minification , mechanics , expression (computer science) , structural engineering , physics , mathematics , computer science , mathematical analysis , algorithm , mathematical optimization , engineering , nonlinear system , quantum mechanics , programming language
Abstract Fast methods for determining the onset of instability for elastic–plastic damage models under multiaxial loading conditions are developed. On the basis of the general Hadamard instability criterion, we derive a closed‐form expression to determine the onset of instability, the bifurcation directions and the polarization vector. The results of the present analytical method are compared with solutions using a numerical minimization method. Excellent agreement and significantly faster computations are achieved for the onset of instability and the directions of the instability mode and the polarization vector when using these new methods. Copyright © 2010 John Wiley & Sons, Ltd.