Homogenized dynamic constitutive relation for Bloch-wave propagation in periodic composites: structure and symmetries
نویسندگان
چکیده
Central to the idea of metamaterials is the concept of dynamic homogenization which seeks to define frequency dependent effective properties for Bloch wave propagation. While the theory of static effective property calculations goes back about 60 years, progress in the actual calculation of dynamic effective properties for periodic composites has been made only very recently. Here we discuss the explicit form of the effective dynamic constitutive equations. We elaborate upon the existence and emergence of coupling in the dynamic constitutive relation and further symmetries of the effective tensors.
منابع مشابه
Wave Propagation Analysis of CNT Reinforced Composite Micro-Tube Conveying Viscose Fluid in Visco-Pasternak Foundation Under 2D Multi-Physical Fields
In this research, wave propagation analysis in polymeric smart nanocomposite micro-tubes reinforced by single-walled carbon nanotubes (SWCNT) conveying fluid is studied. The surrounded elastic medium is simulated by visco-Pasternak model while the composite micro-tube undergoes electro-magneto-mechanical fields. By means of micromechanics method, the constitutive structural coefficients of nano...
متن کاملOn the limit and applicability of dynamic homogenization
Recent years have seen considerable research success in the field of dynamic homogenization which seeks to define frequency dependent effective properties for heterogeneous composites for the purpose of studying wave propagation. There is an approximation involved in replacing a heterogeneous composite with its homogenized equivalent. In this paper we propose a quantification to this approximat...
متن کاملA comparison between two-scale asymptotic expansions and Bloch wave expansions for the homogenization of periodic structures
In this paper we make a comparison between the two-scale asymptotic expansion method for periodic homogenization and the so-called Bloch wave method. It is wellknown that the homogenized tensor coincides with the Hessian matrix of the first Bloch eigenvalue when the Bloch parameter vanishes. In the context of the two-scale asymptotic expansion method, there is the notion of high order homogeniz...
متن کاملNovel nonreciprocal materials based on magnetic photonic crystals
Magnetic photonic crystals are spatially periodic dielectric composites with at least one of the constitutive components being a magnetically polarized material. Magnetic polarization, either spontaneous or induced, is always associated with nonreciprocal circular birefringence (Faraday rotation), which can bring qualitatively new features to the electrodynamics of photonic crystals. If the geo...
متن کاملOverall dynamic constitutive relations of layered elastic composites
A method for the homogenization of a layered elastic composite is presented. It allows direct, consistent, and accurate evaluation of the averaged overall frequency-dependent dynamic material constitutive relations without the need for a point-wise solution of the field equations. When the spatial variation of the field variables is restricted by Bloch-form (Floquet-form) periodicity, then thes...
متن کامل