Analysis of the effective conductivity of composite materials in the entire range of volume fractions of inclusions up to the percolation threshold

2010 ◽  
Vol 41 (6) ◽  
pp. 503-507 ◽  
Author(s):  
Igor V. Andrianov ◽  
Vladyslav V. Danishevs’kyy ◽  
Alexander L. Kalamkarov
Keyword(s):  
Composite Materials ◽  
Percolation Threshold ◽  
Entire Range ◽  
Effective Conductivity ◽  
Volume Fractions

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.

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.

Enhanced Thermal Conductivity of Composite Materials by Filling Sheet and Fiber Under Effect of Filler Contact

2021 ◽  
Author(s):  
Xiao-jian Wang ◽  
Liang-Bi Wang
Keyword(s):  
Thermal Conductivity ◽  
Heat Flux ◽  
Composite Materials ◽  
Thermal Resistance ◽  
Percolation Threshold ◽  
Filler Content ◽  
Interfacial Thermal Resistance ◽  
Combined Effects ◽  
Enhanced Thermal Conductivity ◽  
The Ideal

Abstract The most common non-granular fillers are sheet and fiber. When they are distributed along the heat flux direction, the thermal conductivity of composite increases greatly. Meanwhile, the filler contact also has large effect on the thermal conductivity. However, the effect of filler contact on the thermal conductivity of composite with directional fillers has not been investigated. In this paper, the combined effects of filler contact, content and orientation are investigated. The results show that the effect of filler orientation on the thermal conductivity is greater than filler contact in low filler content, and exact opposite in high filler content. The effect of filler contact on fibrous and sheet fillers is far greater than cube and sphere fillers. This rule is affected by the filler contact. The filler content of 8% is the ideal percolation threshold of composite with fibrous and sheet filler. It is lower than cube filler and previous reports. The space for thermal conductivity growth of composite with directional filler is still very large. The effect of interfacial thermal resistance should be considered in predicting the thermal conductivity of composite under high Rc (>10-4).

Experimental Evaluation of a Steady-State Model for the Wear of Particle-Filled Polymer Composite Materials

1997 ◽  
Vol 119 (4) ◽  
pp. 694-699 ◽  
Author(s):  
Sung Won Han ◽  
Thierry A. Blanchet
Keyword(s):  
Steady State ◽  
Composite Materials ◽  
Wear Rate ◽  
Polymer Composite ◽  
Wear Behavior ◽  
Polymer Composite Materials ◽  
Volume Fractions ◽  
Rule Of Mixtures ◽  
Filler Particles ◽  
Inverse Rule

A model for the steady-state wear behavior of polymer composite materials, including the effects of preferential load support by and surface accumulation of wear-resistant filler particles, is further developed. It is shown that the resultant inverse rule-of-mixtures description of steady-state composite wear rate behavior is independent of the assumed form of filler contact pressure, though preferential load support does affect the degree of surface accumulation of filler particles that occurs. The validity of these descriptions of steady-state wear behavior and surface accumulation as functions of bulk filler volume fraction are investigated by experiments with copper particle-filled PTFE composites for bulk filler volume fractions from 0 to 40 percent. The applicability of the description of surface accumulation for this composite system was limited to bulk filler volume fractions less than 20 percent, a hypothesized result of transition in load-sharing between filler and matrix. The inverse rule-of-mixtures description of steady-state wear rate, however, was maintained over the full range of volume fractions investigated.

Computational Evaluation of Effective Conductivity of Particulate Composites with Imperfect Interfaces

2009 ◽  
Vol 631-632 ◽  
pp. 35-40
Author(s):  
M. Zhang ◽  
Peng Cheng Zhai ◽  
Qing Jie Zhang
Keyword(s):  
Thermal Conductivity ◽  
Effective Thermal Conductivity ◽  
Effective Properties ◽  
Effective Conductivity ◽  
Three Dimensional ◽  
Particulate Composite ◽  
Imperfect Interface ◽  
Particulate Composites ◽  
Imperfect Interfaces ◽  
Volume Fractions

This paper is aimed to numerically evaluate the effective thermal conductivity of randomly distributed spherical particle composite with imperfect interface between the constituents. A numerical homogenization technique based on the finite element method (FEM) with representative volume element (RVE) was used to evaluate the effective properties with periodic boundary conditions. Modified random sequential adsorption algorithm (RSA) is applied to generate the three dimensional RVE models of randomly distributed spheres of identical size with the volume fractions up to 50%. Several investigations have been conducted to estimate the influence of the imperfect interfaces on the effective conductivity of particulate composite. Numerical results reveal that for the given composite, due to the existence of an interfacial thermal barrier resistance, the effective thermal conductivity depends not only on the volume fractions of the particle but on the particle size.

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
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