Abstract
A two-dimensional model of thin-film substrate interactions is obtained from three-dimensional elasticity theory for films having various kinds of crystalline symmetry. Extensions to electro-elastic behaviour are also discussed.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Bibliography
S. S. Antman, Nonlinear Problems of Elasticity. Springer, Berlin, 2005.
E. Baesu, D. Fortune and E. Soós, Incremental behaviour of hyperelastic dielectrics and piezoelectric crystals. ZAMP, 54 160-178, 2003.
P. G. Ciarlet, Mathematical Elasticity, Vol. 1: Three-Dimensional Elasticity. North-Holland, Amsterdam, 1988.
A. C. Eringen and G. A. Maugin, Electrodynamics of Continua, Vol. 1. Springer, N.Y., 1990.
A. E. Green and W. Zerna, Theoretical Elasticity, 2nd edn. Oxford University Press, 1968.
Y. B Fu, Linear and nonlinear wave propagation in coated or uncoated elastic half spaces. Waves in Nonlinear Pre-Stressed Materials (M. Destrade & G. Saccomandi, Eds). CISM Courses and Lecture Notes. Springer, Wien, 2007.
A. Kovetz, Electromagnetic Theory. Oxford University Press, 2000.
J. Merodio and R.W. Ogden, A note on strong ellipticity for transversely isotropic linearly elastic solids. Q. Jl. Mech. Appl. Math. 56, 589-591, 2003.
R. W. Ogden, Non-linear Elastic Deformations. Dover, N.Y., 1997.
G. F. Smith, M. M. Smith and R. S. Rivlin, Integrity bases for a symmetric tensor and a vector: The crystal classes. Arch. Ration. Mech. Anal. 12, 93-133, 1963.
A. J. M. Spencer, Constitutive theory for strongly anisotropic solids, in: Continuum Theory of the Mechanics of Fibre-Reinforced Composites (A.J.M. Spencer, Ed.). CISM Courses and Lectures No. 282, pp. 1-32. Springer, Wien, 1984.
D. J. Steigmann and R. W. Ogden, Surface waves supported by thin-film/substrate interactions. IMA J. Appl. Math., 72, 730-747, 2007.
D. J. Steigmann, Linear theory for the bending and extension of a thin, residually stressed, fiber-reinforced lamina. Int. J. Engng. Sci., 47, 1367-1378, 2009a.
D. J. Steigmann, On the formulation of balance laws for electromagnetic continua. Math. Mech. Solids, 14 390-402, 2009b.
D. J. Steigmann, Elastic waves interacting with a thin, pre-stressed, fiber-reinforced surface film. Int. J. Engng. Sci., 48, 1604-1609, 2010.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 CISM, Udine
About this chapter
Cite this chapter
Steigmann, D.J. (2013). Surface waves in elastic half spaces coated with crystalline films. In: Craster, R.V., Kaplunov, J. (eds) Dynamic Localization Phenomena in Elasticity, Acoustics and Electromagnetism. CISM International Centre for Mechanical Sciences, vol 547. Springer, Vienna. https://doi.org/10.1007/978-3-7091-1619-7_6
Download citation
DOI: https://doi.org/10.1007/978-3-7091-1619-7_6
Publisher Name: Springer, Vienna
Print ISBN: 978-3-7091-1618-0
Online ISBN: 978-3-7091-1619-7
eBook Packages: EngineeringEngineering (R0)