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Published in:
Deformation of a Thin Bonded Transversely Isotropic Elastic Layer Read chapter Read first chapter

2015 | OriginalPaper | Chapter

8. Contact of Thin Inhomogeneous Transversely Isotropic Elastic Layers

Authors : Ivan Argatov, Gennady Mishuris

Published in: Contact Mechanics of Articular Cartilage Layers

Publisher: Springer International Publishing

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Abstract

In this chapter we consider contact problems for thin bonded inhomogeneous transversely isotropic elastic layers. In particular, in Sects. 8.1 and 8.2, the deformation problems are studied for the cases of elastic layers with the out-of-plane and thickness-variable inhomogeneous properties, respectively. In Sect. 8.3, the axisymmetric frictionless contact problems for thin incompressible inhomogeneous elastic layers are studied in detail in the framework of the leading-order asymptotic model. Finally, the deformation problem for a transversely isotropic elastic layer bonded to a rigid substrate, and coated with a very thin elastic layer made of another transversely isotropic material is analyzed in Sect. 8.4.

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previous chapter Articular Contact Mechanics
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Literature
1.
Aleksandrov, V.M.: Asymptotic solution of the axisymmetric contact problem for an elastic layer of incompressible material. J. Apll. Math. Mech. 67, 589–593 (2003)CrossRef
2.
Alexandrov, V.M., Mkhitaryan, S.M.: Contact Problems for Solids with Thin Coatings and Layers [in Russian]. Nauka, Moscow (1985)
3.
Alexandrov, V.M., Pozharskii, D.A.: Three-Dimensional Contact Problems. Kluwer, Dordrecht (2001)MATHCrossRef
4.
Argatov, I., Mishuris, G.: An asymptotic model for a thin bonded elastic layer coated with an elastic membrane. arXiv preprint arXiv:​1504.​06792 (2015)
5.
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
6.
Avilkin, V.I., Alexandrov, V.M., Kovalenko, E.V.: On using the more-accurate equations of thin coatings in the theory of axisymmetric contact problems for composite foundations. J. Appl. Math. Mech. 49, 770–777 (1985)MATHCrossRef
7.
Barber, J.R.: Contact problems for the thin elastic layer. Int. J. Mech. Sci. 32, 129–132 (1990)MATHCrossRef
8.
9.
Elliott, H.A.: Three-dimensional stress distributions in hexagonal aeolotropic crystals. Math. Proc. Camb. Phil. Soc. 44, 522–533 (1948)CrossRef
10.
11.
Federico, F., Herzog, W.: Towards an analytical model of soft biological tissues. J. Biomech. 41, 3309–3313 (2008)MathSciNetCrossRef
12.
Federico, S., Grillo, A., La Rosa, G., Giaquinta, G., Herzog, W.: A transversely isotropic, transversely homogeneous microstructural-statistical model of articular cartilage. J. Biomech. 38, 2008–2018 (2005)CrossRef
13.
Gladwell, G.M.L.: Contact Problems in the Classical Theory of Elasticity. Sijthoff and Noordho, Alphen aan den Rijn (1980)MATHCrossRef
14.
Gol’denveizer, A.L.: Derivation of an approximate theory of bending of a plate by the method of asymptotic integration of the equations of the theory of elasticity. J. Appl. Math. Mech. 26, 1000–1025 (1962)MathSciNetCrossRef
15.
16.
Malits, P.: Indentation of an incompressible inhomogeneous layer by a rigid circular indenter. Q. J. Mech. Appl. Math. 59, 343–358 (2006)MATHMathSciNetCrossRef
17.
Rahman, M., Newaz, G.: Elastostatic surface displacements of a half-space reinforced by a thin film due to an axial ring load. Int. J. Eng. Sci. 35, 603–611 (1997)MATHCrossRef
18.
Rahman, M., Newaz, G.: Boussinesq type solution for a transversely isotropic half-space coated with a thin film. Int. J. Eng. Sci. 38, 807–822 (2000)MATHCrossRef
19.
Timoshenko, S.P., Goodier, J.N.: Theory of Elasticity. McGraw-Hill, New York (1970)MATH
Metadata
Title
Contact of Thin Inhomogeneous Transversely Isotropic Elastic Layers
Authors
Ivan Argatov
Gennady Mishuris
Copyright Year
2015
Book
Contact Mechanics of Articular Cartilage Layers

Print ISBN: 978-3-319-20082-8

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

Copyright Year: 2015

DOI
https://doi.org/10.1007/978-3-319-20083-5_8

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