Localization and Bifurcation Analysis of Granular Materials in Micropolar Continuum
Publication: International Journal of Geomechanics
Volume 19, Issue 7
Abstract
The onset of strain localization is indicated by the weak-discontinuity bifurcation condition—namely, the determinant of the acoustic tensor must be zero. In this study, the analytical solution of the acoustic tensors in plane-strain condition was derived for both the Cauchy-Boltzmann continuum and the micropolar continuum. A typical elastoplastic constitutive model based on the Drucker-Prager criterion was implemented in Abaqus by utilizing its user-defined material (UMAT) and user-defined element (UEL) options. The validity of the localization condition was verified and compared for the Cauchy-Boltzmann continuum and the micropolar continuum through the plane-strain numerical experiments. Results showed that the determinant of the acoustic tensor in the micropolar continuum tended to a constant value when the localization occurred rather than tending to zero as in the Cauchy-Boltzmann continuum. This indicates that the micropolar continuum can prevent the ill-posed solution when bifurcation occurs; in contrast, the onset of localization in the micropolar continuum is totally the same as that in the Cauchy-Boltzmann continuum.
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Acknowledgments
The authors acknowledge the support of this work by the National Natural Science Foundation of China (51709176) and the scientific researching fund of the Educational Commission of Hebei Province of China (Z2017018).
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Published In
International Journal of Geomechanics
Volume 19 • Issue 7 • July 2019
Copyright
© 2019 American Society of Civil Engineers.
History
Received: Dec 21, 2017
Accepted: Dec 28, 2018
Published online: Apr 18, 2019
Published in print: Jul 1, 2019
Discussion open until: Sep 18, 2019
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