A quasi-static stability analysis for Biot’s equation and standard dissipative systems
Article dans une revue avec comité de lecture
URI
http://www.sciencedirect.com/science/article/pii/S0997753806000799http://hdl.handle.net/10985/10335
Date
2007Journal
European Journal of Mechanics - A/SolidsAbstract
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.
Files in this item
Related items
Showing items related by title, author, creator and subject.
-
Communication avec acteABED-MERAIM, Farid; NGUYEN, Quoc Son (Société Marocaine des Sciences Mécaniques, 2007)Cette étude est consacrée à la stabilité de la réponse quasi-statique de systèmes standard dissipatifs (visco-élastiques, visco-plastiques ou élasto-plastiques). Dans le cas de solides visqueux (visco-élastiques ou ...
-
Communication avec acteFRANZ, Gérald; ABED-MERAIM, Farid; BEN ZINEB, Tarak; BERVEILLER, Marcel; LEMOINE, Xavier (2006)La striction et la rupture au cours de l’opération d’emboutissage figurent parmi les principaux phénomènes limitant les déformations maximales admises par les métaux. Ces phénomènes sont liés à la microstructure des matériaux ...
-
Communication sans acteTIAN, Haitao; POTIER-FERRY, Michel; ABED-MERAIM, Farid (AJM Ferreira et al., 2017)This paper introduces a new meshless method named Taylor Meshless Method (TMM) using Taylor series to deduce the shape functions. Next the problem is discretized by point-collocation only on the boundary and without ...
-
Article dans une revue avec comité de lectureTIAN, Haitao; POTIER-FERRY, Michel; ABED-MERAIM, Farid (2021)Buckling and wrinkling of thin structures often lead to very complex response curves that are hard to follow by standard path-following techniques, especially for very thin membranes in a slack or nearly slack state. Many ...
-
Article dans une revue avec comité de lectureHADDAG, Badis; ABED-MERAIM, Farid; BALAN, Tudor (Elsevier, 2009)Sheet metal forming processes generally involve large deformations together with complex loading sequences. In order to improve numerical simulation predictions of sheet part forming, physically-based constitutive models ...