[Construction dʼun bipotentiel représentant une loi linéaire non associée]
Nous considérons un matériau dont la relation contraintes–déformations est linéaire, mais pas symétrique. La recherche dʼun potentiel étant vaine, nous tentons de représenter la loi de comportement par un bipotentiel. La méthode de Fitzpatrick conduit à construire une suite croissante appropriée de bipotentiels. La technique est illustrée sur lʼexemple des lois coaxiales.
We consider a material whose stress–strain relation is linear but not symmetrical. As the research of a potential is futile, we attempt to represent the constitutive law by a bipotential. Fitzpatrick method leads us to construct a suitable increasing sequence of bipotentials. The technique is exemplified on coaxial constitutive laws.
Accepté le :
Publié le :
Mot clés : Lois de comportement non associées, Matériaux non standard, Matériaux standard implicites, Matériaux n-monotones, Bipotentiels
@article{CRMECA_2013__341_9-10_667_0,
author = {Arjdal El Hanafi and Jamal Chaoufi and Claude Vall\'ee and Arnaud Germaneau and Kossi Atchonouglo and Hassan Fatmaoui and Abdelaaziz Ghafiri},
title = {Construction of a bipotential representing a linear non-associated constitutive law},
journal = {Comptes Rendus. M\'ecanique},
pages = {667--671},
publisher = {Elsevier},
volume = {341},
number = {9-10},
year = {2013},
doi = {10.1016/j.crme.2013.09.002},
language = {en},
}
TY - JOUR AU - Arjdal El Hanafi AU - Jamal Chaoufi AU - Claude Vallée AU - Arnaud Germaneau AU - Kossi Atchonouglo AU - Hassan Fatmaoui AU - Abdelaaziz Ghafiri TI - Construction of a bipotential representing a linear non-associated constitutive law JO - Comptes Rendus. Mécanique PY - 2013 SP - 667 EP - 671 VL - 341 IS - 9-10 PB - Elsevier DO - 10.1016/j.crme.2013.09.002 LA - en ID - CRMECA_2013__341_9-10_667_0 ER -
%0 Journal Article %A Arjdal El Hanafi %A Jamal Chaoufi %A Claude Vallée %A Arnaud Germaneau %A Kossi Atchonouglo %A Hassan Fatmaoui %A Abdelaaziz Ghafiri %T Construction of a bipotential representing a linear non-associated constitutive law %J Comptes Rendus. Mécanique %D 2013 %P 667-671 %V 341 %N 9-10 %I Elsevier %R 10.1016/j.crme.2013.09.002 %G en %F CRMECA_2013__341_9-10_667_0
Arjdal El Hanafi; Jamal Chaoufi; Claude Vallée; Arnaud Germaneau; Kossi Atchonouglo; Hassan Fatmaoui; Abdelaaziz Ghafiri. Construction of a bipotential representing a linear non-associated constitutive law. Comptes Rendus. Mécanique, Volume 341 (2013) no. 9-10, pp. 667-671. doi : 10.1016/j.crme.2013.09.002. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2013.09.002/
[1] Generalized standard media and variational principles in classical and finite strain elastoplasticity, J. Mech. Phys. Solids, Volume 45 (1997) no. 5, pp. 667-688
[2] On the generalized standard materials, J. Méc., Volume 14 (1975), pp. 39-63 (in French)
[3] Application of convex analysis to the treatment of elasto-plastic systems (P. Germain; B. Nayroles, eds.), Applications of Methods of Functional Analysis to Problems in Mechanics, Lecture Notes in Mathematics, vol. 503, Springer, Berlin, 1976
[4] Legendre–Fenchel duality in elasticity, C. R. Acad. Sci. Paris, Ser. I, Volume 349 (2011) no. 9–10, pp. 597-602
[5] Convex functionals, Séminaire Jean-Leray. Sur les équations aux dérivées partielles, vol. 2, Collège de France, Paris, 1966, pp. 1-108 http://archive.numdam.org (in French) 2003. Reprint: Istituto poligrafico e zecca dello stato S.p.A., Roma
[6] Non maximal cyclically monotone graphs and construction of a bipotential for the Coulombʼs dry friction law, J. Convex Anal., Volume 17 (2010) no. 1, pp. 81-94
[7] Implicit standard materials (D. Weichert; G. Maier, eds.), Inelastic Behaviour of Structures under Variable Repeated Loads — Direct Analysis Methods, CISM Courses and Lectures IV, vol. 432, International Centre for Mechanical Sciences, Springer, Vienna, New York, 2002
[8] Shakedown with non-associated flow rule (D. Weichert; G. Maier, eds.), Inelastic Behaviour of Structures under Variable Repeated Loads — Direct Analysis Methods, CISM Courses and Lectures IV, vol. 432, International Centre for Mechanical Sciences, Springer, Vienna, New York, 2002
[9] Fitzpatrick function, cyclic monotonicity and Rockafellar antiderivative, Nonlinear Anal., Volume 66 (2007), pp. 1198-1223
[10] Representing a non–associated constitutive law by a bipotential issued from a Fitzpatrick sequence, Arch. Mech., Volume 61 (2009) no. 3–4, pp. 325-340
[11] A class of non-associated materials: n-monotone materials — Hookeʼs Law of elasticity revisited, J. Elast., Volume 112 (2013) no. 2, pp. 111-138
[12] Representing monotone operators by convex functions, Workshop/Miniconference on Functional Analysis and Optimization, Canberra (S.P. Fitzpatrick; J.R. Giles, eds.) (Proceedings of the Centre for Mathematical Analysis of the Australian National University), Volume vol. 20 ( August 8–24, 1988 ), pp. 59-65
[13] Pseudo-potentials and bipotentials: A constructive procedure for non-associated plasticity and unilateral contact, Discrete Contin. Dyn. Syst., Ser. S, Volume 6 (2013) no. 2, pp. 567-590
[14] Structural stability of rate-independent nonpotential flows, Discrete Contin. Dyn. Syst., Ser. S, Volume 6 (2013) no. 1, pp. 257-275
[15] Variational formulation and structural stability of monotone equations, Calc. Var. Partial Differ. Equ., Volume 47 (2013) no. 1–2, pp. 273-317
Cité par Sources :
Commentaires - Politique
Modelling of orthogonal cutting by incremental elastoplastic analysis and meshless method
Elhassan Boudaia; Lahbib Bousshine; Hicham Fassi Fihri; ...
C. R. Méca (2009)
Jean-Paul Penot
C. R. Math (2004)