Abstract
Stability and bifurcation analyses are discussed here for time-independent standard dissipative systems of materials and structures. This discussion is illustrated by some simple applications in plasticity and fracture mechanics.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Bazant, Z.; Cedolin, L.; Stability of Structures: Elastic, Plastic, Fracture and Damage Theories; Oxford University Press.
Bérest, P. Problèmes de Mécanique Associés au Stockage Souterrain, Thèse de l’Ecole des Mines.
Biot, M.A. Mechanics of Incremental Deformation, Wiley, New York.
Cochelin, B.; Potier-Ferry, M.; Interaction entre les flambages locaux et la propagation du délaminage dans les composites. Calcul des structures et intelligences artificielles. Pluralis, Paris.
Cottle, R.; Pang, J.S.; Stone, R.E.; The linear complementary problem; Academic Press.
Dems, K; Mroz, Z.; Stability condition for brittle plastic structures with propagating damage surfaces. J. Struc. Mech., 13:95–122.
Destuynder, P.; Nevers, T.; Un modèle de calcul des forces de délaminage dans les plaques minces. J. Mec. Th. Appl.; 6:179–207.
Ehrlacher, A.; Contribution à l’étude thermodynamique de la progression de fissure et à la mécanique de l’endommagement brutal. Thèse d’Etat, Paris.
Gao, H.J.; Rice, J.; Somewhat circular tensile crack. Int. J. Fracture; 33:155–174.
Germain, P.; Cours de Mécanique des Milieux Continus; Masson, Paris.
Halphen, B; Nguyen, Q.S.; Sur les matériaux standard généralisés. J. Mécanique; 14:1–37.
Hill, R.; A general theory of uniqueness and stability in elastic/plastic solid; J. Mech. Phys. Solids; 6:236–249.
Hutchinson, JW.; Thouless, M.D.; Liniger, E.G.; Growth and configurational stability of circular buckling driven thin film delamination. Act. Metal. Mat.; 40:455–466.
Jensen, H.M.; Thouless, M.D.; Buckling instability of stable edge cracks. J. Appl. Mech., 62:620–625.
Leblond, J.B.; Mouchrif, S.E.; Perrin, G.; The tensile tunnel crack with a slightly wavy form. Int. J. Solids Structures; 33:1995–2022.
Lemaitre, J.; Chaboche, J.L.; Mécanique des Matériaux Solides. Dunod, Paris.
Mandel, J.; Plasticité Classique et Visco-plasticité. CISM, Springer-Verlag, Wien.
Maugin, G.A.; The thermomechnics of plasticity and fracture; Cambridge University Press.
Moreau, J.J.; On unilateral constraints, friction and plasticity; CIME, Springer-Verlag, Wien.
Nguyen, Q.S.; Bifurcation and stability in dissipative media (plasticity, fracture, friction); Appl. Mech. Rev., 47:1–31.
Nguyen, Q.S.; Stolz, C.; Debruyne, G.; Energy methods in fracture mechanics: stability, bifurcation and second variation; Eur. J. Mech.;9:157–173.
Nguyen, Q.S. Stabilité et Mécanique Non Linéaire, Hermes, Paris.
Petryk, H.; On energy criteria of plastic nstability. Plastic instability, Considère mem.; ENPC-Presses, Paris.
Pradeilles-Duval, R.M.; Evolution des systèmes avec frontières de discontinuité mobiles. Thèse, Ecole Polytechnique; Paris.
Storakers, B.; Nonlinear aspects of delamination in structural members. Proceedings ICTAM, Springer-Verlag, Berlin.
Suo, X.Z.; Combescure, A.; Second variation of energy and an associated line-independent integral in fracture mechanics. Eur. J. Mech., 11:609–624.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2000 Kluwer Academic Publishers
About this chapter
Cite this chapter
Nguyen, QS. (2000). Standard dissipative systems and stability analysis. In: Maugin, G.A., Drouot, R., Sidoroff, F. (eds) Continuum Thermomechanics. Solid Mechanics and Its Applications, vol 76. Springer, Dordrecht. https://doi.org/10.1007/0-306-46946-4_26
Download citation
DOI: https://doi.org/10.1007/0-306-46946-4_26
Publisher Name: Springer, Dordrecht
Print ISBN: 978-0-7923-6407-8
Online ISBN: 978-0-306-46946-6
eBook Packages: Springer Book Archive