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

Titre traduit de la contribution: Condition suffisante d'instabilité linéaire pour les matériaux viscoplastiques

Nicolas Triantafyllidis
, Patrick Massin
, Yves M. Leroy

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

Résultats de recherche: Contribution à un journal › Article › Revue par des pairs

Résumé

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.

Titre traduit de la contribution	Condition suffisante d'instabilité linéaire pour les matériaux viscoplastiques
langue originale	Anglais
Pages (de - à)	151-157
Nombre de pages	7
journal	Comptes Rendus de l'Academie de Sciences - Serie IIb: Mecanique, Physique, Chimie, Astronomie
Volume	324
Numéro de publication	3
Les DOIs	https://doi.org/10.1016/s1251-8069(99)80019-0
état	Publié - 1 janv. 1997
Modification externe	Oui

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10.1016/s1251-8069(99)80019-0

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A sufficient condition for the linear instability of strain-rate-dependent solids. / Triantafyllidis, Nicolas; Massin, Patrick; Leroy, Yves M.
Dans: Comptes Rendus de l'Academie de Sciences - Serie IIb: Mecanique, Physique, Chimie, Astronomie, Vol 324, Numéro 3, 01.01.1997, p. 151-157.

Résultats de recherche: Contribution à un journal › Article › Revue par des pairs

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T1 - A sufficient condition for the linear instability of strain-rate-dependent solids

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AU - Massin, Patrick

AU - Leroy, Yves M.

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

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