Keywords
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
H. B. HUNTINGTON, The Elastic Constants of Crystals, Solid State Reprints, Academic Press, NY, 1958.
M. AVELLANEDA, A. V. CHERKAEV, K. A. LURIE, G. W. MILTON, On the effective conductivity of polycrystals and a three-dimensional phase-interchange inequality, J. App. Phys., May 15, 1988.
M. AVELLANEDA, G. W. MILTON, Optimal bounds on the effective bulk modulus of polycrystals, to appear in SIAM Jour. Appl. Math.
G. W. MILTON, Microgeometries corresponding exactly with effective medium theories, in: Physics and Chemistry of Porous Media, Johnson and Sen, Eds., AIP Conf. # 107, American Institute of Physics, NY, 1984.
G. W. MILTON, The coherent potential approximation is a realizable effective medium scheme, Comm. Math. Physics, 99, 463–500, 1985.
M. AVELLANEDA, Iterated homogenization, differential effective medium theory, and applications, Comm. in Pure and Appl. Math., Vol. XL, 527–554, 1987.
A. BENSOUSSAN, J. L.LIONS, G. PAPANICOLAOU, Asymptotic Analysis of Periodic Structures, North-Holland, 1978.
W. VOIGT, Lehrbuch der Krystallphysik, Teubner, Berlin, 1910.
J. R. WILLIS, Variational and related methods for the overall properties of composites, in: Advances in Applied Mechanics 21, Yih, ed., Academic Press, New York, 1981.
K. SCHULGASSER, Bounds on the conductivity of statistically isotropic polycrystals, J. Phys. C, 10, 1977, p. 407–417.
K. SCHULGASSER, Sphere assemblage model for polycrystals and symmetric materials, J. Appl. Phys. 54, 1982, p. 1380.
J. BALL, J. C. CURRIE and P. J. OLVER, Null Lagrangians, weak continuity and variational problems of arbitrary order, Jour. Func. Anal. 41, 1981.
F. MURAT, Compacité par compensation: condition nécessaire et suffisante de continuité sous hypothèse de rang constant, Ann. Sc. Norm. Sup. Pisa 8, 1981, p. 69.
G. W. MILTON and E. NESI, private communication on cyclic microstructures.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1989 International Federation for Information Processing
About this paper
Cite this paper
Avellaneda, M. (1989). Iterated homogenization and the effective properties of polycrystals. In: Simon, J. (eds) Control of Boundaries and Stabilization. Lecture Notes in Control and Information Sciences, vol 125. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0043353
Download citation
DOI: https://doi.org/10.1007/BFb0043353
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-51239-4
Online ISBN: 978-3-540-46181-4
eBook Packages: Springer Book Archive