nach oben

Erschienen in:

2015 | OriginalPaper | Buchkapitel

4. Frictionless Contact of Thin Viscoelastic Layers

verfasst von : Ivan Argatov, Gennady Mishuris

Erschienen in: Contact Mechanics of Articular Cartilage Layers

Verlag: Springer International Publishing

Einloggen

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

search-config

KI-gestützte Suche

Aus

Abstract

The chapter begins with an introduction to linear viscoelastic theory, and then proceeds to a generalization of the elastic leading-order asymptotic models for the viscoelastic case, based on the correspondence principle. In Sect. 4.2, we consider the main features of the analytical technique for solving unilateral contact problems for a viscoelastic foundation. The axisymmetric contact problem for a thin bonded incompressible viscoelastic layer is analyzed in Sect. 4.3 and in the refined formulation accounting for tangential displacements in Sect. 4.4. Finally, in Sect. 4.5 we solve the problem of frictionless contact for thin incompressible viscoelastic layers bonded to rigid substrates shaped like elliptic paraboloids.

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

Vorheriges Kapitel Unilateral Frictionless Contact of Thin Bonded Incompressible Elastic Layers

Nächstes Kapitel Linear Transversely Isotropic Biphasic Model for Articular Cartilage Layer

Ateshian, G.A., Lai, W.M., Zhu, W.B., Mow, V.C.: An asymptotic solution for the contact of two biphasic cartilage layers. J. Biomech. 27, 1347–1360 (1994)CrossRef

Argatov, I.I.: Asymptotic modeling of the impact of a spherical indenter on an elastic half-space. Int. J. Solids Struct. 45, 5035–5048 (2008)MATHCrossRef

Argatov, I.: A general solution of the axisymmetric contact problem for biphasic cartilage layers. Mech. Res. Comm. 38, 29–33 (2011)MATHCrossRef

Argatov, I.I.: Development of an asymptotic modeling methodology for tibio-femoral contact in multibody dynamic simulations of the human knee joint. Multibody Syst. Dyn. 28, 3–20 (2012)MATHMathSciNetCrossRef

Argatov, I.I., Mishuris, G.S.: Axisymmetric contact problem for a biphasic cartilage layer with allowance for tangential displacements on the contact surface. Eur. J. Mech. A/Solids 29, 1051–1064 (2010)MathSciNetCrossRef

Argatov, I., Mishuris, G.: Elliptical contact of thin biphasic cartilage layers: exact solution for monotonic loading. J. Biomech. 44, 759–761 (2011)CrossRef

Argatov, I., Mishuris, G.: Frictionless elliptical contact of thin viscoelastic layers bonded to rigid substrates. Appl. Math. Model. 35, 3201–3212 (2011)MATHMathSciNetCrossRef

Barber, J.R.: Contact problems for the thin elastic layer. Int. J. Mech. Sci. 32, 129–132 (1990)MATHCrossRef

Belokon’, A.V., Vorovich, I.I.: Contact problems of the linear theory of viscoelasticity ignoring friction and cohesion forces [in Russian]. Izv. Akad. Nauk SSSR. MTT [Mechanics of Solids], 6, 63–73 (1973)

10.

Chadwick, R.S.: Axisymmetric indentation of a thin incompressible elastic layer. SIAM J. Appl. Math. 62, 1520–1530 (2002)MATHMathSciNetCrossRef

11.

Christensen, R.M.: Theory of Viscoelasticity. Academic Press, New York (1982)

12.

Graham, G.A.C.: The contact problem in the linear theory of viscoelasticity. Int. J. Eng. Sci. 3, 27–46 (1965)MATHCrossRef

13.

Hoang, S.K., Abousleiman, Y.N.: Poroviscoelasticity of transversely isotropic cylinders under laboratory loading conditions. Mech. Res. Commun. 37, 298–306 (2010)MATHCrossRef

14.

Jaffar, M.J.: Asymptotic behaviour of thin elastic layers bonded and unbonded to a rigid foundation. Int. J. Mech. Sci. 31, 229–235 (1989)CrossRef

15.

Korhonen, R.K., Laasanen, M.S., Töyräs, J., Rieppo, J., Hirvonen, J., Helminen, H.J., Jurvelin, J.S.: Comparison of the equilibrium response of articular cartilage in unconfined compression, confined compression and indentation. J. Biomech. 35, 903–909 (2002)

16.

Kravchuk, A.S.: On the Hertz problem for linearly and nonlinearly elastic bodies of finite dimensions. J. Appl. Math. Mech. 41, 320–328 (1977)MathSciNetCrossRef

17.

Lakes, R.S.: Viscoelastic Materials. Cambridge University Press, Cambridge (2009)CrossRef

18.

Lee, E.H., Radok, J.R.M.: The contact problem for viscoelastic bodies. J. Appl. Mech. 27, 438–444 (1960)MATHMathSciNetCrossRef

19.

Mishuris, G., Argatov, I.: Exact solution to a refined contact problem for biphasic cartilage layers. In: Nithiarasu, P., Löhner, R. (eds.) Proceedings of the 1st International Conference on Mathematical and Computational Biomedical Engineering—CMBE2009, pp. 151–154. Swanseak, UK, June 29–July 1 2009

20.

Naghieh, G.R., Jin, Z.M., Rahnejat, H.: Contact characteristics of viscoelastic bonded layers. Appl. Math. Model. 22, 569–581 (1998)CrossRef

21.

Naghieh, G.R., Rahnejat, H., Jin, Z.M.: Characteristics of frictionless contact of bonded elastic and viscoelastic layered solids. Wear 232, 243–249 (1999)CrossRef

22.

Pipkin, A.C.: Lectures on Viscoelastic Theory. Springer, New York (1986)CrossRef

23.

Ting, T.C.T.: Contact problems in the linear theory of viscoelasticity. J. Appl. Mech. 35, 248–254 (1968)MATHCrossRef

24.

Tschoegl, N.W.: Time dependence in material properties: an overview. Mech. Time-Depend. Mat. 1, 3–31 (1997)CrossRef

25.

Wu, J.Z., Herzog, W., Epstein, M.: An improved solution for the contact of two biphasic cartilage layers. J. Biomech. 30, 371–375 (1997)CrossRef

Titel: Frictionless Contact of Thin Viscoelastic Layers
verfasst von: Ivan Argatov
Gennady Mishuris
Verlag: Springer International Publishing
Buch: Contact Mechanics of Articular Cartilage Layers
Print ISBN: 978-3-319-20082-8

Electronic ISBN: 978-3-319-20083-5

Copyright-Jahr: 2015
DOI: https://doi.org/10.1007/978-3-319-20083-5_4

Premium Partner

Marktübersichten

Die im Laufe eines Jahres in der „adhäsion“ veröffentlichten Marktübersichten helfen Anwendern verschiedenster Branchen, sich einen gezielten Überblick über Lieferantenangebote zu verschaffen.

Zur Marktübersicht