ANALYTICAL AND NUMERICAL RESULTS FOR THE EFFECTIVE CONDUCTIVITY OF 2D COMPOSITE MATERIALS WITH RANDOM POSITION OF CIRCULAR REINFORCEMENTS

2009 ◽  
Author(s):  
E.V. PESETSKAYA ◽  
T. FIEDLER ◽  
A. ÖCHSNER ◽  
J. GRÁCIO ◽  
S.V. ROGOSIN
Keyword(s):  
Composite Materials ◽  
Effective Conductivity ◽  
Numerical Results ◽  
Random Position

scholarly journals Geometric series expansion of the Neumann–Poincaré operator: Application to composite materials

2021 ◽  
pp. 1-26
Author(s):  
ELENA CHERKAEV ◽  
MINWOO KIM ◽  
MIKYOUNG LIM
Keyword(s):  
Composite Materials ◽  
Series Expansion ◽  
Function Theory ◽  
Effective Conductivity ◽  
Two Dimensions ◽  
Boundary Integral ◽  
Geometric Function Theory ◽  
Boundary Integral Formulation ◽  
Geometric Function ◽  
Series Expression

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.

Using quasiconvex functionals to bound the effective conductivity of composite materials

1993 ◽  
Vol 123 (4) ◽  
pp. 633-679 ◽  
Author(s):  
V. Nesi
Keyword(s):  
Composite Materials ◽  
Arbitrary Number ◽  
Effective Conductivity ◽  
Spatial Dimension ◽  
Conductivity Tensor ◽  
Volume Fractions

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.

The effective conductivity of composite materials with cubic arrays of multi-coated spheres

2003 ◽  
Vol 77 (3-4) ◽  
pp. 441-448 ◽  
Author(s):  
A. Moosavi ◽  
P. Sarkomaa ◽  
W. Polashenski Jr
Keyword(s):  
Composite Materials ◽  
Effective Conductivity ◽  
Coated Spheres

scholarly journals Centrifugal stresses in arbitrarily laminated, rectangular—anistropic circular discs

1975 ◽  
Vol 10 (2) ◽  
pp. 84-92 ◽  
Author(s):  
C W Bert
Keyword(s):  
Composite Materials ◽  
Closed Form ◽  
Linear Theory ◽  
Closed Form Solution ◽  
Form Solution ◽  
Numerical Results ◽  
Current Interest ◽  
Elastic Plates ◽  
Organic Fibre ◽  
Anisotropic Elastic

The problem is formulated as one in the linear theory of thin, laminated, anisotropic elastic plates. A direct force-and-moment formulation is used, simplifying approximation is introduced and a closed-form solution is obtained. This solution exhibits bending-stretching coupling if the plate is asymmetrically laminated with respect to mass or stiffness or both. Numerical results typical of certain composite materials of current interest are presented. Specific laminates considered as examples include (1) glass—epoxy/steel, (2) cross-ply graphite—epoxy, and (3) various quasi-isotropic layups of organic fibre—epoxy.

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