Abstract
Some recent advances in the theory of dynamic materials are listed in the paper. We discuss the technique used to determine the set of invariant characteristics of material mixtures in one spatial dimension and time, in the context of electrodynamics of moving dielectrics, versus the relevant results in traditional electrostatics. Some special features of dynamic materials demonstrated through a material design are advertised as well. Among them, we mention the possibility to eliminate the cut-off frequency in the waveguides with activated dielectric filling.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
I.I. Blekhman and K.A. Lurie, On dynamic materials. Proc. of the Russian Academy of Sciences (Doklady) 37 (2000) 182–185.
K.A. Lurie, The problem of effective parameters of a mixture of two isotropic dielectrics distributed in space-time and the conservation law for wave impedance in one-dimensional wave propagation. Proc. Roy. Soc. London A 454 (1998) 1767–1779.
K.A. Lurie, Control of the coefficients of linear hyperbolic equations via spatio-temporal composites. In: V. Berdichevsky, V. Jikov and G. Papanicolaou (eds), Homogenization. World Scientific, Singapore (1999) pp. 285–315.
B.P. Lavrov, Private Communication. Mekhanobr-Tekhnika, St. Petersburg, Russia (2002).
A.M. Dykhne, Conductivity of a two-dimensional two-phase system. Soviet Phys. JETP 32 (1971) 63–65.
K.A. Lurie, Bounds for the electromagnetic material properties of a spatio-temporal dielectric polycrystal with respect to one-dimensional wave propagation. Proc. Roy. Soc. London A 456 (2000) 1547–1557.
K.A. Lurie and A.V. Cherkaev, Effective characteristics of composite materials and the optimal design of structural elements. In: A. Cherkaev and R. Kohn (eds), Topics in the Mathematical Modelling of Composite Materials. Birkhäuser, Boston (1997) pp. 175–258.
K.A. Lurie and S.L.Weekes, Effective and averaged energy densities in one-dimensional wave propagation through spatio-temporal dielectric laminates with negative effective values of ε and µ. To appear in: R. Agarwal and D. O'Reagan (eds), Nonlinear Analysis and Applications. World Scientific, Singapore (2003).
K.A. Lurie, A stable spatio-temporal G-closure and Gm-closure of a set of isotropic dielectrics with respect to one-dimensional wave propagation. Submitted to Wave Motion.
K.A. Lurie, Effective properties of smart elastic laminates and the screening phenomenon. Internat. J. Solids Struct. 34 (1997) 1633–1643.
C.A. Truesdell III, A First Course in Rational Continuum Mechanics, Part I. Academic Press, New York, 1977.
A.I. Lurie, Non-linear Theory of Elasticity (in Russian). Nauka, Moscow, 1980 (English translation: Non-linear Theory of Elasticity. North Holland, Amsterdam, New York, Oxford, Tokyo, 1990).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Lurie, K.A. Some New Advances in the Theory of Dynamic Materials. Journal of Elasticity 72, 229–239 (2003). https://doi.org/10.1023/B:ELAS.0000018780.82718.19
Issue Date:
DOI: https://doi.org/10.1023/B:ELAS.0000018780.82718.19