A quasi-static stability analysis for Biot’s equation and standard dissipative systems
dc.contributor.author
hal.structure.identifier | NGUYEN, Quoc Son
|
dc.contributor.author
hal.structure.identifier | ABED-MERAIM, Farid
|
dc.date.accessioned | 2015 |
dc.date.available | 2015 |
dc.date.issued | 2007 |
dc.date.submitted | 2015 |
dc.identifier.issn | 0997-7538 |
dc.identifier.uri | http://www.sciencedirect.com/science/article/pii/S0997753806000799 |
dc.identifier.uri | http://hdl.handle.net/10985/10335 |
dc.description.abstract | In this paper, an extended version of Biot's differential equation is considered in order to discuss the quasi-static stability of a response for a solid in the framework of generalized standard materials. The same equation also holds for gradient theories since the gradients of arbitrary order of the state variables and of their rates can be introduced in the expression of the energy and of the dissipation potentials. The stability of a quasi-static response of a system governed by Biot's equations is discussed. Two approaches are considered, by direct estimates and by linearizations. The approach by direct estimates can be applied in visco-plasticity as well as in plasticity. A sufficient condition of stability is proposed and based upon the positivity of the second variation of energy along the considered response. This is an extension of the criterion of second variation, well known in elastic buckling, into the study of the stability of a response. The linearization approach is available only for smooth dissipation potentials, i.e. for the study of visco-elastic solids and leads to a result on asymptotic stability. The paper is illustrated by a simple example. |
dc.language.iso | en |
dc.publisher | Elsevier |
dc.rights | Post-print |
dc.subject | Biot's equation |
dc.subject | Generalized standard models |
dc.subject | Local and non-local descriptions |
dc.subject | Plasticity |
dc.subject | Second variation criterion |
dc.subject | Stability of a quasi-static response |
dc.subject | Visco-plasticity |
dc.title | A quasi-static stability analysis for Biot’s equation and standard dissipative systems |
dc.identifier.doi | 10.1016/j.euromechsol.2006.06.005 |
dc.typdoc | Article dans une revue avec comité de lecture |
dc.localisation | Centre de Metz |
dc.subject.hal | Sciences de l'ingénieur: Matériaux |
dc.subject.hal | Sciences de l'ingénieur: Mécanique |
dc.subject.hal | Sciences de l'ingénieur: Mécanique: Génie mécanique |
dc.subject.hal | Sciences de l'ingénieur: Mécanique: Matériaux et structures en mécanique |
dc.subject.hal | Sciences de l'ingénieur: Mécanique: Mécanique des matériaux |
dc.subject.hal | Sciences de l'ingénieur: Mécanique: Mécanique des solides |
dc.subject.hal | Sciences de l'ingénieur: Mécanique: Mécanique des structures |
ensam.audience | Internationale |
ensam.page | 383-393 |
ensam.journal | European Journal of Mechanics - A/Solids |
ensam.volume | 26 |
ensam.issue | 3 |
hal.identifier | hal-00105164 |
hal.version | 1 |
hal.date.transferred | 2020-04-08T16:00:05Z |
hal.submission.permitted | True |
hal.status | accept |