nach oben

Erschienen in:

2015 | OriginalPaper | Buchkapitel

Variational and Hemivariational Inequalities in Mechanics of Elastoplastic, Granular Media, and Quasibrittle Cracks

verfasst von : Boris D. Annin, Victor A. Kovtunenko, Vladimir M. Sadovskii

Erschienen in: Analysis, Modelling, Optimization, and Numerical Techniques

Verlag: Springer International Publishing

Einloggen

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config

KI-gestützte Suche

Aus

Abstract

This contribution is devoted to the mathematical theory of elastoplastic and granular solids as well as the quasibrittle fracture of nonlinear cracks. Basic variational and hemivariational inequalities describing nonlinear phenomena due to plasticity, internal friction, interfacial interaction, and alike dissipative physics are outlined from the point of view of nonsmooth and nonconvex optimization. Primary results of the nonlinear theory and its application to solid mechanics are surveyed.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

über 102.000 Bücher
über 537 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Finance + Banking
Management + Führung
Marketing + Vertrieb
Maschinenbau + Werkstoffe
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 390 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Maschinenbau + Werkstoffe

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 340 Zeitschriften

aus folgenden Fachgebieten:

Bauwesen + Immobilien
Business IT + Informatik
Finance + Banking
Management + Führung
Marketing + Vertrieb
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Vorheriges Kapitel Minimizing Sign Changes Rowwise: Consecutive Ones Property and Beyond

Nächstes Kapitel Effects of a Discrete Time Delay on an HIV Pandemic

Annin, B.D., Cherepanov, G.P.: Elastic–Plastic Problems. ASME, New York (1998)

Annin, B.D., Sadovskii, V.M.: On the numerical realization of a variational inequality in problems of the dynamics of elastoplastic bodies. Comput. Math. Math. Phys. 36, 1313–1324 (1996)MATHMathSciNet

Annin, B.D., Sadovsky, V.M.: A numerical analysis of laminated elastic-plastic plates under dynamic loading. Compos. Sci. Technol. 45, 241–246 (1992)CrossRef

Annin, B.D., Sadovskaya, O.V., Sadovskii, V.M.: Dynamic contact problems of elastoplasticity. Problems Mater. Sci. 33, 426–434 (2003)

Antipin, A.: Splitting of the gradient approach for solving extremal inclusions. Comput. Math. Math. Phys. 38, 1069–1082 (1998)MATHMathSciNet

Baniotopoulos, C.C., Haslinger, J., Moravkova, Z.: Mathematical modeling of delamination and nonmonotone friction problems by hemivariational inequalities. Appl. Math. 50, 1–25 (2005)CrossRefMATHMathSciNet

Bychek, O.V., Sadovskii, V.M.: On the investigation of the dynamic contact interaction of deformable bodies. J. Appl. Mech. Tech. Phys. 39, 628–633 (1998)CrossRefMathSciNet

Dal Maso, G., Iurlano, F.: Fracture models as Γ-limits of damage models. Commun. Pure Appl. Anal. 12, 1657–1686 (2013).CrossRefMATHMathSciNet

Fortin, D., Tseveendorj, I.: Q-subdifferential and Q-conjugate for global optimality. Comput. Math. Math. Phys. 54, 265–274 (2014)CrossRefMathSciNet

10.

Fremiot, G., Horn, W., Laurain, A., Rao, M., Sokolowski, J.: On the analysis of boundary value problems in nonsmooth domains. Dissertationes Mathematicae, Inst. Math. Polish Acad. Sci., vol. 462, Warsaw (2009)

11.

Hintermüller, M., Kovtunenko, V.A., Kunisch, K.: Obstacle problems with cohesion: A hemi-variational inequality approach and its efficient numerical solution. SIAM J. Optim. 21, 491–516 (2011)CrossRefMATHMathSciNet

12.

Itou, H., Kovtunenko, V.A., Tani, A.: The interface crack with Coulomb friction between two bonded dissimilar elastic media. Appl. Math. 56, 69–97 (2011)CrossRefMATHMathSciNet

13.

Khludnev, A.M., Kovtunenko, V.A.: Analysis of Cracks in Solids. WIT-Press, Southampton (2000)

14.

Khludnev, A.M., Kovtunenko, V.A., Tani, A.: On the topological derivative due to kink of a crack with non-penetration. Anti-plane model. J. Math. Pures Appl. 94, 571–596 (2010)CrossRefMATHMathSciNet

15.

Khludnev, A.M., Leugering, G.: Optimal control of cracks in elastic bodies with thin rigid inclusions. ZAMM Z. Angew. Math. Mech. 91, 125–137 (2011)CrossRefMATHMathSciNet

16.

Khludnev, A.M., Sokolowski, J.: Modelling and Control in Solid Mechanics. Birkhäuser, Basel (1997)MATH

17.

Kovtunenko, V.A.: Nonconvex problem for crack with nonpenetration. Z. Angew. Math. Mech. 85, 242–251 (2005)CrossRefMATHMathSciNet

18.

Kovtunenko, V.A.: Primal-dual methods of shape sensitivity analysis for curvilinear cracks with non-penetration. IMA J. Appl. Math. 71, 635–657 (2006) [AQ4]CrossRefMATHMathSciNet

19.

Kovtunenko, V.A.: A hemivariational inequality in crack problems. Optimization 60, 1071–1089 (2011)CrossRefMATHMathSciNet

20.

Kovtunenko, V.A., Sukhorukov, I.V.: Optimization formulation of the evolutionary problem of crack propagation under quasibrittle fracture. Appl. Mech. Tech. Phys. 47, 704–713 (2006)CrossRefMathSciNet

21.

Leugering, G., Prechtel, M., Steinmann, P., Stingl, M.: A cohesive crack propagation model: Mathematical theory and numerical solution. Commun. Pure Appl. Anal. 12, 1705–1729 (2013)CrossRefMATHMathSciNet

22.

Mielke, A., Truskinovsky, L.: From discrete visco-elasticity to continuum rate-independent plasticity: Rigorous results. Arch. Ration. Mech. Anal. 203, 577–619 (2012)CrossRefMATHMathSciNet

23.

Myasnikov, V.P., Sadovskii, V.M.: Variational principles of the theory of limit equilibrium of media with different strengths. J. Appl. Math. Mech. 68, 437–446 (2004)CrossRefMathSciNet

24.

Oralbekova, Zh.O., Iskakov, K.T., Karchevsky, A.L.: Existence of the residual functional derivative with respect to a coordinate of gap point of medium. Appl. Comput. Math. 12, 222–233 (2013)

25.

Ovcharova, N., Gwinner, J.: A study of regularization techniques of nondifferentiable optimization in view of application to hemivariational inequalities. J. Optim. Theory Appl. 162, 754–778 (2014).MATHMathSciNet

26.

Plotnikov, P.I., Rudoy, E.M.: Shape sensitivity analysis of energy integrals for bodies with rigid inclusions and cracks. Dokl. Math. 84, 681–684 (2011).CrossRefMATHMathSciNet

27.

Radwan, A., Vasilieva, O., Enkhbat, R., Griewank, A., Guddat, J.: Parametric approach to optimal control. Optim. Lett. 6, 1303–1316 (2012)CrossRefMATHMathSciNet

28.

Sadovskaya, O.V., Sadovskii, V.M.: On the theory of finite deformations of a granular medium. J. Appl. Math. Mech. 71, 93–110 (2007)CrossRefMathSciNet

29.

Sadovskaya, O., Sadovskii, V.: Mathematical Modeling in Mechanics of Granular Materials. Springer, Berlin (2012)CrossRefMATH

30.

Sadovskii, V.M.: Discontinuous Solutions in Dynamic Elastic-Plastic Problems. Fizmatlit, Moscow (1997) (in Russian)

Titel: Variational and Hemivariational Inequalities in Mechanics of Elastoplastic, Granular Media, and Quasibrittle Cracks
verfasst von: Boris D. Annin
Victor A. Kovtunenko
Vladimir M. Sadovskii
Verlag: Springer International Publishing
Buch: Analysis, Modelling, Optimization, and Numerical Techniques
Print ISBN: 978-3-319-12582-4

Electronic ISBN: 978-3-319-12583-1

Copyright-Jahr: 2015
DOI: https://doi.org/10.1007/978-3-319-12583-1_3

Springer Professional

Abstract

Bitte loggen Sie sich ein, um Zugang zu Ihrer Lizenz zu erhalten.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Springer Professional "Technik"

Springer Professional "Wirtschaft"

Premium Partner