Three-Dimensional Multiscale Bifurcation Analysis of Granular Media
Publication: Journal of Engineering Mechanics
Volume 135, Issue 6
Abstract
This paper deals with Hill’s bifurcation criterion, which is very well suited to describe various failure modes in granular media. The first part of this paper is dedicated to the analytical and numerical investigation of this criterion by considering phenomenological constitutive relations: the incrementally piece-wise linear and nonlinear relations proposed by Darve. The 3D bifurcation domain and 3D cones of unstable directions are given for these two relations. A similar analysis is performed with a micromechanical model in the second part of the article. Finally, a qualitative comparison of the results obtained with these two different approaches leads us to some key conclusions about this material instability criterion, which is studied for the first time for general 3D conditions, by considering these nonconventional constitutive relations.
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Acknowledgments
The writers of this paper are grateful to the French Ministries of Research and Civil Engineering (RGCU) for the support provided through the national research projects: PIR (Rock Instabilities Prevention), SIGMA-ANR 2005 and STABROCK-ANR 2005. The French Federative Research Structure RNVO (Natural Hazards and Structure Vulnerability) is also gratefully acknowledged by the writers.
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Information & Authors
Information
Published In
Journal of Engineering Mechanics
Volume 135 • Issue 6 • June 2009
Pages: 493 - 509
Copyright
© 2009 ASCE.
History
Received: Apr 22, 2008
Accepted: Sep 17, 2008
Published online: Mar 6, 2009
Published in print: Jun 2009
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