Effective conductivity of composite materials with random positions of cylindrical inclusions: finite number inclusions in the cell

2005 ◽  
Vol 84 (8) ◽  
pp. 843-865 ◽  
Author(s):  
Ekaterina V. Pesetskaya *
Author(s):  
ELENA CHERKAEV ◽  
MINWOO KIM ◽  
MIKYOUNG LIM

The Neumann–Poincaré (NP) operator, a singular integral operator on the boundary of a domain, naturally appears when one solves a conductivity transmission problem via the boundary integral formulation. Recently, a series expression of the NP operator was developed in two dimensions based on geometric function theory [34]. In this paper, we investigate geometric properties of composite materials using this series expansion. In particular, we obtain explicit formulas for the polarisation tensor and the effective conductivity for an inclusion or a periodic array of inclusions of arbitrary shape with extremal conductivity, in terms of the associated exterior conformal mapping. Also, we observe by numerical computations that the spectrum of the NP operator has a monotonic behaviour with respect to the shape deformation of the inclusion. Additionally, we derive inequality relations of the coefficients of the Riemann mapping of an arbitrary Lipschitz domain using the properties of the polarisation tensor corresponding to the domain.


Author(s):  
V. Nesi

SynopsisIn this paper we establish bounds constraining the effective conductivity tensor of composites made of an arbitrary number n of possibly anisotropic phases in prescribed volume fractions. The bounds are valid in any spatial dimension d≧2. The bounds have a very simple and concise form and include those previously obtained by Hashin and Shtrikman, Murat and Tartar, Lurie and Cherkaev, Kohn and Milton, Avellaneda, Cherkaev, Lurie and Milton and Dell'Antonio and Nesi.


2003 ◽  
Vol 77 (3-4) ◽  
pp. 441-448 ◽  
Author(s):  
A. Moosavi ◽  
P. Sarkomaa ◽  
W. Polashenski Jr

2021 ◽  
Author(s):  
Uğur Gökmen ◽  
Zübeyde Özkan ◽  
Sema Bilge Ocak

Abstract Gamma-ray and neutron shielding properties of the AA6082 + TiO2 (0-50wt.%) functionally graded composite materials (FGCMs) were investigated using the PSD software. The values of the mean free path (MFP), half-value layer (HVL), linear attenuation coefficients (LAC), mass attenuation coefficient (MAC), tenth-value layer (TVL), exposure buildup factors (EBF), effective atomic number (Zeff), effective conductivity (Ceff), and fast neutron removal cross-sections (FNRC) were found for the energy range between 0.015–15 MeV. The increase in the TiO2 content in the AA6082 composite material has raised the values of MAC and LAC. The calculations for the EBFs were carried out using the G-P fitting method for the energy range between 0.015–15 MeV and penetration depth of up to 40 mfp. The results revealed that HVL values ranged between 0.01-0.116 cm, TVL values ranged between 0.01-0.385 cm, FNRC values ranged between 7.918-10.017 cm-1, and Ceff values ranged between 5.67 x1010 and 9.85x1010 S/m. The AA6082 + TiO2 (50%) composite material was observed to provide the maximum photon and neutron shielding capacity since it offered the highest Zeff, MAC, and FNRC values, and the lowest HVL value. In terms of several aspects, the research is considered original. Besides contributing to several technologies including nanotechnology and space technologies, present research’s results may contribute to nuclear technology.


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