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.
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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.
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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
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DOI: https://doi.org/10.1007/978-3-319-65346-4_4
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