Journal
INTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS
Volume 31, Issue 8, Pages 1007-1032Publisher
WILEY
DOI: 10.1002/nag.573
Keywords
bifurcation; stability; controllability; dry liquefaction; large deformations; second-order work
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In this paper, the ability of a material rate-independent system to evolve toward another mechanical state from an equilibrium configuration, with no change in the control parameters, is investigated. From a mechanical point of view, this means that the system can spontaneously develop kinetic energy with no external disturbance from an equilibrium state, which corresponds to a particular case of bifurcation. The existence of both conjugate incremental strain and stress such that the second-order work vanishes is established as a necessary and sufficient condition for the appearance of this bifurcation phenomenon. It is proved that this fundamental result is independent of the constitutive relation of the rate-independent material considered. Then the case of homogeneous loading paths is investigated, and, as an illustration, the subsequent results are applied to interpret the well-known liquefaction observed under isochoric triaxial loading conditions with loose granular materials. Copyright (c) 2006 John Wiley & Sons, Ltd.
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