Abstract
This chapter is about G-closures (i.e., the sets of invariant properties) of the regular mixtures of two isotropic dielectrics distributed in 1D + time. It begins with the conservation law of the wave impedance through one-dimensional wave propagation along a DM-polycrystal. This is a kinetic laminate assembled in 1D + time of fragments of the same dielectric brought into a relative longitudinal motion. This conservation law is then extended to any regular assembly of two arbitrary (activated or kinetic) dielectrics in 1D + time. G-closure of any number of such dielectrics can be characterized on the basis of this law. Some special features of dynamic G-closures are discussed through the comparison with similar results known in the static conditions.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
In [1], the term “absolutely stable” was introduced instead of “uniformly stable.” In this text we prefer the latter term as conceptually more appropriate.
References
Dykhne, A.M.: Conductivity of a two-dimensional two-phase systems. Sov. Phys. JETP 32, 63–65 (1971)
Lurie, K.A.: A stable spatio-temporal G-closure and G m -closure of a set of isotropic dielectrics with respect to one-dimensional wave propagation. Wave Motion 40, 95–110 (2004)
Lurie, K.A., Cherkaev, A.V.: Exact estimates of conductivity of composites formed by two isotropically conducting media taken in prescribed proportion. Proc. R. Soc. Edinburgh A 99(1–2), 71–87 (1984)
Lurie, K.A., Cherkaev, A.V.: G-closure of a set of anisotropically conducting media in the two-dimensional case. J. Optim. Theory Appl. 42, 283–304 (1984); Corrig. 53, 319 (1987)
Lurie, K.A., Fedorov, A.V., Cherkaev, A.V.: On the existence of solutions to some problems of optimal design for bars and plates. Ioffe Institute Technical Report 668, Leningrad, p. 43 (1980); also J. Optim. Theory Appl. 42, 247–282 (1984)
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2017 Springer International Publishing AG
About this chapter
Cite this chapter
Lurie, K.A. (2017). G-Closures of a Set of Isotropic Dielectrics with Respect to One-Dimensional Wave Propagation. In: An Introduction to the Mathematical Theory of Dynamic Materials. Advances in Mechanics and Mathematics, vol 15. Springer, Cham. https://doi.org/10.1007/978-3-319-65346-4_4
Download citation
DOI: https://doi.org/10.1007/978-3-319-65346-4_4
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-65345-7
Online ISBN: 978-3-319-65346-4
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)