Dynamic effective properties of heterogeneous geological formations with spherical inclusions under periodic time variations

2013 ◽  
Vol 40 (7) ◽  
pp. 1345-1350 ◽  
Author(s):  
A. Rabinovich ◽  
G. Dagan ◽  
T. Miloh
Keyword(s):  
Effective Properties ◽  
Spherical Inclusions ◽  
Time Variations ◽  
Geological Formations ◽  
Dynamic Effective Properties

Determination of effective properties of granite rock: A numerical investigation

MRS Advances ◽  
2018 ◽  
Vol 3 (37) ◽  
pp. 2159-2168
Author(s):  
Rehema Ndeda ◽  
S. E. M Sebusang ◽  
R. Marumo ◽  
Erich O. Ogur
Keyword(s):  
Elastic Properties ◽  
Close Agreement ◽  
Effective Properties ◽  
Volume Element ◽  
The Finite Element Method ◽  
Effective Elastic Properties ◽  
Spherical Inclusions ◽  
Periodic Microstructures ◽  
Crack Profile

ABSTRACTMacroscopic strength of the rock depends on the behavior of the micro constituents, that is, the minerals, pores and crack profile. It is important to determine the effect of these constituents on the overall behavior of the rock. This study seeks to estimate the effective elastic properties of granite using the finite element method. A representative volume element (RVE) of suitable size with spherical inclusions of different distribution is subjected to loading and the effective elastic properties determined. The results are compared to those obtained from analytical methods. The elastic properties are obtained in both the axial and transverse direction to account for anisotropy. It is observed that there is congruence in the results obtained both analytically and numerically. The method of periodic microstructures exhibits close agreement with the numerical results.

Effective Dynamic Properties of Microstructured Heterogeneous Materials

2012 ◽  
Author(s):  
Ankit Srivastava ◽  
Sia Nemat-Nasser
Keyword(s):  
Wave Propagation ◽  
Explicit Form ◽  
Constitutive Equations ◽  
Effective Properties ◽  
Dynamic Properties ◽  
Effective Property ◽  
Bloch Wave ◽  
Periodic Composites ◽  
Effective Dynamic ◽  
Dynamic Effective Properties

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.

scholarly journals Sub-wavelength plasmonic crystals: dispersion relations and effective properties

2010 ◽  
Vol 466 (2119) ◽  
pp. 1993-2020 ◽  
Author(s):  
Santiago P. Fortes ◽  
Robert P. Lipton ◽  
Stephen P. Shipman
Keyword(s):  
Dispersion Relation ◽  
Dielectric Permittivity ◽  
Effective Properties ◽  
Plasma Frequency ◽  
Power Series Expansion ◽  
Sobolev Norm ◽  
Radius Of Convergence ◽  
Plasmonic Crystals ◽  
Dynamic Effective Properties ◽  
Sub Wavelength

We obtain a convergent power series expansion for the first branch of the dispersion relation for sub-wavelength plasmonic crystals consisting of plasmonic rods with frequency-dependent dielectric permittivity embedded in a host medium with unit permittivity. The expansion parameter is η = kd =2 πd / λ , where k is the norm of a fixed wavevector, d is the period of the crystal and λ is the wavelength, and the plasma frequency scales inversely to d , making the dielectric permittivity in the rods large and negative. The expressions for the series coefficients (also called dynamic correctors) and the radius of convergence in η are explicitly related to the solutions of higher order cell problems and the geometry of the rods. Within the radius of convergence, we are able to compute the dispersion relation and the fields and define dynamic effective properties in a mathematically rigorous manner. Explicit error estimates show that a good approximation to the true dispersion relation is obtained using only a few terms of the expansion. The convergence proof requires the use of properties of the Catalan numbers to show that the series coefficients are exponentially bounded in the H 1 Sobolev norm.

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