Abstract
We discuss the effect of inclusion shape on the dielectric and elastic properties of two-dimensional materials. We show how the dielectric constant is determined by the dipole moment of the inclusion, conveniently found from the far field. Conformai mapping techniques are useful in two-dimensions to obtain the changes in the bulk properties in the special cases when the inclusions are holes or perfectly conducting or rigid. Our results are interpreted in terms of the reciprocity theorem for dielectrics and in terms of a similar, recently proved, theorem for elastic materials. We illustrate these techniques for polygonal inclusions and compare our results with those for circles and ellipses.
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.
Similar content being viewed by others
References
Cherkaev, A., Lurie, K. and Milton, G. W. (1992) Invariant properties of the stress in plane elasticity and equivalence classes of composites, Proc. Roy. Soc. A 438, 519–529.
Day, A. R., Synder, K. A., Garboczi, E. J. and Thorpe, M. F. (1992) The elastic moduli of a sheet containing circular holes, J. Mech. Phys. Solids 40, 1031–1051.
Gibiansky, L. V. and Torquato, S. (1993) Link between the conductivity and elastic moduli of compoisite materials, Phys. Rev. Letts. 71, 2927–2930.
Gibiansky, L. V. and Torquato, S. (1993) Link between the conductivity and elastic moduli of compoisite materials, Phys. Rev. Letts. 71, 2927–2930.
Jasiuk, I., Chen, J. and Thorpe, M. F. (1994) Elastic moduli of two dimensional materials with polygonal and elliptical holes, Applied Mechanics Reviews 47 (1, Part 2), S18–S28.
Hetherington, J. H. and Thorpe, M. F. (1992) The conductivity of a sheet containing inclusions with sharp corners, Proc. Roy. Soc. A 438, 591–604.
Kachanov, M., Tsukrov, I. and Shafiro, B. (1994) Effective moduli of a solid with holes and cavities of various shapes, Applied Mechanics Reviews 47 (1, Part 2), S151–S174.
Keller, J. B. (1964) A theorem on the conductivity of a composite medium, J. Math Phys. 5, 548–549.
Maple V Release 2. Waterloo Maple Software, Copyright (c) 1981–1992 by the University of Waterloo
Savin, G. N. (1961) Stress concentration around holes, Kreiger Publishing Co., Malabar, Florida.
Sen, P. N. and Thorpe, M. F. (1985) Elastic moduli of two-dimensional composite continua with elliptical inclusions, J. Accoust. Soc. Am. 77, 1674–1680.
Thorpe, M. F. (1992) The conductivity of a sheet containing a few polygonal holes and/or superconducting inclusions, Proc. Roy. Soc. A 437, 221–227.
Thorpe, M. F. and Jasiuk, I. M. (1992) New results in the theory of elasticity for two-dimensional composites, Proc. Roy. Soc. A 438, 531–544.
Zimmerman, R. W. (1986) Compressibility of two dimensional cavities of various shapes, J. Appl. Mech. 53, 500–504.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1995 Springer Science+Business Media Dordrecht
About this paper
Cite this paper
Thorpe, M.F., Chen, J., Jasiuk, I.M. (1995). Properties of two-Dimensional Materials Containing Inclusions of Various Shapes. In: Pyrz, R. (eds) IUTAM Symposium on Microstructure-Property Interactions in Composite Materials. Solid Mechanics and Its Applications, vol 37. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-0059-5_30
Download citation
DOI: https://doi.org/10.1007/978-94-011-0059-5_30
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-4031-0
Online ISBN: 978-94-011-0059-5
eBook Packages: Springer Book Archive