A quasi-static stability analysis for Biot's equation and standard dissipative systems - Archive ouverte HAL Access content directly
Journal Articles European Journal of Mechanics - A/Solids Year : 2007

A quasi-static stability analysis for Biot's equation and standard dissipative systems

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.
Fichier principal
Vignette du fichier
LEM3_EJMSOL_2007_ABEDMERAIM.pdf (139.96 Ko) Télécharger le fichier
Origin : Files produced by the author(s)
Loading...

Dates and versions

hal-00105164 , version 1 (08-04-2020)

Identifiers

Cite

Farid Abed-Meraim, Quoc Son Nguyen. A quasi-static stability analysis for Biot's equation and standard dissipative systems. European Journal of Mechanics - A/Solids, 2007, 26 (3), pp.383-393. ⟨10.1016/j.euromechsol.2006.06.005⟩. ⟨hal-00105164⟩
462 View
163 Download

Altmetric

Share

Gmail Facebook X LinkedIn More