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On the numerical resolution of the discontinuous material bifurcation problem
Author(s) -
Oliver J.,
Huespe A. E.,
Cante J. C.,
Díaz G.
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.2870
Subject(s) - bifurcation , eigenvalues and eigenvectors , mathematics , tangent , resolution (logic) , homogeneous space , numerical analysis , mathematical analysis , computer science , geometry , nonlinear system , physics , quantum mechanics , artificial intelligence
The work focuses on the numerical resolution of the discontinuous material bifurcation problem as a relevant ingredient in computational material failure mechanics. The problem consists of finding the conditions for the strain localization onset in terms of the so‐called bifurcation time, localization directions and localization modes. A numerical algorithm, based on the iterative resolution of a coupled eigenvalue problem in terms of the localization tensor, is proposed for such purpose. The algorithm is shown to be always convergent to the exact solution for the symmetric case (major and minor symmetries of the tangent constitutive operator). In the unsymmetric case (only minor symmetries), the solution is no longer exact, although it is shown that using the symmetric part of the localization tensor in the proposed algorithms provides enough accurate solutions for most of cases. Numerical examples illustrate the benefits of the proposed methodology in terms of accuracy and savings in the computational cost associated with the problem. Copyright © 2010 John Wiley & Sons, Ltd.