A sufficient condition for the linear instability of strain-rate-dependent solids

Nicolas Triantafyllidis; Patrick Massin; Yves M. Leroy

doi:10.1016/s1251-8069(99)80019-0

A sufficient condition for the linear instability of strain-rate-dependent solids

Nicolas Triantafyllidis
, Patrick Massin
, Yves M. Leroy

University of Michigan, Ann Arbor
Lamsid/EDF/R and D
Department of Mechanics École Polytechnique

Research output: Contribution to journal › Article › peer-review

Abstract

The linear stability criterion proposed generalizes to continua earlier results obtained for the viscoplastic Shanley column. A sufficient condition for instability is marked by the change of sign of the real part of the dominant eigenvalue for the system of equations constructed from the linearized version of the first and second derivatives with respect to time of the principle of virtual work. In particular, it is shown that the conditions for first instability are those for the first bifurcation of a strain-rate-independent solid obtained in the limit of inviscid plastic flow.

Translated title of the contribution	Condition suffisante d'instabilité linéaire pour les matériaux viscoplastiques
Original language	English
Pages (from-to)	151-157
Number of pages	7
Journal	Comptes Rendus de l'Academie de Sciences - Serie IIb: Mecanique, Physique, Chimie, Astronomie
Volume	324
Issue number	3
DOIs	https://doi.org/10.1016/s1251-8069(99)80019-0
Publication status	Published - 1 Jan 1997
Externally published	Yes

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abstract = "The linear stability criterion proposed generalizes to continua earlier results obtained for the viscoplastic Shanley column. A sufficient condition for instability is marked by the change of sign of the real part of the dominant eigenvalue for the system of equations constructed from the linearized version of the first and second derivatives with respect to time of the principle of virtual work. In particular, it is shown that the conditions for first instability are those for the first bifurcation of a strain-rate-independent solid obtained in the limit of inviscid plastic flow.",

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AU - Massin, Patrick

AU - Leroy, Yves M.

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Y1 - 1997/1/1

N2 - The linear stability criterion proposed generalizes to continua earlier results obtained for the viscoplastic Shanley column. A sufficient condition for instability is marked by the change of sign of the real part of the dominant eigenvalue for the system of equations constructed from the linearized version of the first and second derivatives with respect to time of the principle of virtual work. In particular, it is shown that the conditions for first instability are those for the first bifurcation of a strain-rate-independent solid obtained in the limit of inviscid plastic flow.

AB - The linear stability criterion proposed generalizes to continua earlier results obtained for the viscoplastic Shanley column. A sufficient condition for instability is marked by the change of sign of the real part of the dominant eigenvalue for the system of equations constructed from the linearized version of the first and second derivatives with respect to time of the principle of virtual work. In particular, it is shown that the conditions for first instability are those for the first bifurcation of a strain-rate-independent solid obtained in the limit of inviscid plastic flow.

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DO - 10.1016/s1251-8069(99)80019-0

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JO - Comptes Rendus de l'Academie de Sciences - Serie IIb: Mecanique, Physique, Chimie, Astronomie

JF - Comptes Rendus de l'Academie de Sciences - Serie IIb: Mecanique, Physique, Chimie, Astronomie

IS - 3

ER -

A sufficient condition for the linear instability of strain-rate-dependent solids

Abstract

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