On the numerical resolution of the discontinuous material bifurcation problem

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, localizati...

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Veröffentlicht in:International journal for numerical methods in engineering Jg. 83; H. 6; S. 786 - 804
Hauptverfasser: Oliver, J., Huespe, A. E., Cante, J. C., Díaz, G.
Format: Journal Article Verlag
Sprache:Englisch
Veröffentlicht: Chichester, UK John Wiley & Sons, Ltd 06.08.2010
Wiley
Schlagworte:
Algorismes numèrics
Algorithms
Anàlisi numèrica
Bifurcations
computational material failure
discontinuous material bifurcation
Exact sciences and technology
Fracture mechanics (crack, fatigue, damage...)
Fundamental areas of phenomenology (including applications)
Inelasticity (thermoplasticity, viscoplasticity...)
Localization
Matemàtiques i estadística
Mathematical analysis
Mathematical models
Mathematics
Methods of scientific computing (including symbolic computation, algebraic computation)
Mètodes numèrics
Numerical analysis
Numerical analysis. Scientific computation
Numerical methods and algorithms
Physics
Position (location)
Sciences and techniques of general use
Solid mechanics
strain localization
Structural and continuum mechanics
Tensors
Àrees temàtiques de la UPC
Deformation band
Constitutive equation
Localized mode
Rupture
Iterative method
Modeling
Exact solution
strain localization
Inelasticity
discontinuous material bifurcation
Eigenvalue problem
Localization
computational material failure
ISSN:0029-5981, 1097-0207, 1097-0207
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Beschreibung
Zusammenfassung: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.
Bibliographie:istex:731806270ABD1F43820D86C88D8C30E94A0B650E
Spanish Ministry of Science and Innovation - No. BIA2008-00411
ark:/67375/WNG-MSV6509R-3
ArticleID:NME2870
ObjectType-Article-2
SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 23
ISSN:0029-5981
1097-0207
1097-0207
DOI:10.1002/nme.2870