Estimation of the physical properties of nanocomposites by finite-element discretization and Monte Carlo simulation
28 Jun 2013-Philosophical Transactions of the Royal Society A (The Royal Society)-Vol. 371, Iss: 1993, pp 20120494-20120494
TL;DR: This paper reviews and enhances numerical models for determining thermal, elastic and electrical properties of carbon nanotube-reinforced polymer composites and validated by comparison with various experimental datasets reported in the recent literature.
Abstract: This paper reviews and enhances numerical models for determining thermal, elastic and electrical properties of carbon nanotube-reinforced polymer composites. For the determination of the effective ...
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01 Jan 1997
TL;DR: This chapter introduces the finite element method (FEM) as a tool for solution of classical electromagnetic problems and discusses the main points in the application to electromagnetic design, including formulation and implementation.
Abstract: This chapter introduces the finite element method (FEM) as a tool for solution of classical electromagnetic problems. Although we discuss the main points in the application of the finite element method to electromagnetic design, including formulation and implementation, those who seek deeper understanding of the finite element method should consult some of the works listed in the bibliography section.
1,820 citations
01 Jan 2008
TL;DR: In this article, the electrical properties of polymer nanocomposites containing a small amount of carbon nanotube (CNT) were successfully predicted based on three-dimensional (3D) statistical percolation and 3D resistor network modeling.
Abstract: The electrical properties of polymer nanocomposites containing a small amount of carbon
nanotube (CNT) are remarkably superior to those of conventional electronic composites. Based on three-dimensional (3D) statistical percolation and 3D resistor network modeling, the electrical properties of CNT nanocomposites, at and after percolation, were successfully predicted in this work. The numerical analysis was also extended to investigate the effects of the aspect ratio, the electrical conductivity, the aggregation and the shape of CNTs on the electrical properties of the nanocomposites. A simple empirical model was also established based on present numerical simulations to predict the electrical conductivity in several electronic composites with various fillers. This investigation further highlighted the importance
of theoretical and numerical analyses in the exploration of basic physical phenomena, such as percolation and conductivity in novel nanocomposites.
291 citations
TL;DR: In this paper, the authors provide a consolidated review of the imminent prospects of utilizing carbon nanotubes and nanoparticles in aerospace sciences, based on their recent implementations and predicted future applications.
188 citations
TL;DR: In this article, the authors highlight and categorize the most important and novel studies conducted to explore the mechanical behavior of nano-composites reinforced with carbon nanotubes (CNTs).
112 citations
TL;DR: A new set of algorithms is introduced for the virtual reconstruction of heterogeneous material microstructures, in which morphologies of embedded particles/fibers are explicitly represented, and several example problems are presented to show the application of these algorithms.
43 citations
Cites background or methods from "Estimation of the physical properti..."
...For fibrous microstructures, a Weibull distribution function [41] is utilized to quantify the distribution of lengths of embedded fibers as...
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...4, and within the range of 20 nm to 500 nm [41]....
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References
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TL;DR: In this paper, a method of calculating the average internal stress in the matrix of a material containing inclusions with transformation strain is presented. But the authors do not consider the effects of the interaction among the inclusions and of the presence of the free boundary.
7,000 citations
"Estimation of the physical properti..." refers methods in this paper
...Seidel & Lagoudas [38] modelled nanotubes using a composite cylinders approach, and used the Mori–Tanaka method [39] to obtain effective elastic properties for the composite as a whole....
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TL;DR: The tensile strengths of individual multiwalled carbon nanotubes (MWCNTs) were measured with a "nanostressing stage" located within a scanning electron microscope and a variety of structures were revealed, such as a nanotube ribbon, a wave pattern, and partial radial collapse.
Abstract: The tensile strengths of individual multiwalled carbon nanotubes (MWCNTs) were measured with a “nanostressing stage” located within a scanning electron microscope. The tensile-loading experiment was prepared and observed entirely within the microscope and was recorded on video. The MWCNTs broke in the outermost layer (“sword-in-sheath” failure), and the tensile strength of this layer ranged from 11 to 63 gigapascals for the set of 19 MWCNTs that were loaded. Analysis of the stress-strain curves for individual MWCNTs indicated that the Young's modulus E of the outermost layer varied from 270 to 950 gigapascals. Transmission electron microscopic examination of the broken nanotube fragments revealed a variety of structures, such as a nanotube ribbon, a wave pattern, and partial radial collapse.
5,011 citations
"Estimation of the physical properti..." refers methods in this paper
...[69,70] performed tensile load testing using an atomic force microscopy tip to document the nonlinear stress–strain relationship of SWCNTs....
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IBM1
TL;DR: In this article, an extension of percolation theory to treat transport is described, and a general expression for the conductance of such networks is derived, which relates to the spin-stiffness coefficient of dilute ferromagnet.
Abstract: Extensions of percolation theory to treat transport are described. Resistor networks, from which resistors are removed at random, provide the natural generalization of the lattice models for which percolation thresholds and percolation probabilities have previously been considered. The normalized conductance, $G$, of such networks proves to be a sharply defined quantity with a characteristic concentration dependence near threshold which appears sensitive only to dimensionality. Numerical results are presented for several families of $3D$ and $2D$ network models. Except close to threshold, the models based on bond percolation are accurately described by a simple effective medium theory, which can also treat continuous media or situations less drastic than the percolation models, for example, materials in which local conductivity has a continuous distribution of values. The present calculations provide the first quantitative test of this theory. A "Green's function" derivation of the effective medium theory, which makes contact with similar treatments of disordered alloys, is presented. Finally, a general expression for the conductance of a percolation model is obtained which relates $G$ to the spin-stiffness coefficient, $D$, of an appropriately defined model dilute ferromagnet. We use this relationship to argue that the "percolation channels" through which the current flows above threshold must be regarded as three dimensional.
4,342 citations
"Estimation of the physical properti..." refers background or methods in this paper
...Several authors [14,45,55,56] emphasized the impact of the number of CNT contact points on the results....
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...Kirkpatrick [45] was the first to prove the viability of a resistor network model in determining the electrical properties of a system of random sticks....
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...By relocating the parts of fibres extending outside the sample to the opposite boundary, continuity between sample structures was maintained, insulating boundary conditions were validated, and the structure was representative of an infinite system [45,51]....
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...One of the original resistor network models was developed by Kirkpatrick [45] as an extension to established lattice models....
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...Kirkpatrick [45] was among the first to use KCL on two- and three-dimensional site and bond percolation models based on 19 rsta.royalsocietypublishing.org PhilTransRSocA371:20120494 ...................................................... RA3 RA2 RB2 RB1 RA1 fibre A fibre B AB cR Figure 12....
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Book•
01 Jan 1984
TL;DR: Second-order Differential Equations in One Dimension: Finite Element Models (FEM) as discussed by the authors is a generalization of the second-order differential equation in two dimensions.
Abstract: 1 Introduction 2 Mathematical Preliminaries, Integral Formulations, and Variational Methods 3 Second-order Differential Equations in One Dimension: Finite Element Models 4 Second-order Differential Equations in One Dimension: Applications 5 Beams and Frames 6 Eigenvalue and Time-Dependent Problems 7 Computer Implementation 8 Single-Variable Problems in Two Dimensions 9 Interpolation Functions, Numerical Integration, and Modeling Considerations 10 Flows of Viscous Incompressible Fluids 11 Plane Elasticity 12 Bending of Elastic Plates 13 Computer Implementation of Two-Dimensional Problems 14 Prelude to Advanced Topics
3,043 citations
TL;DR: An unusually high value, lambda approximately 6600 W/m K, is suggested for an isolated (10,10) nanotube at room temperature, comparable to the thermal conductivity of a hypothetical isolated graphene monolayer or diamond.
Abstract: Recently discovered carbon nanotubes have exhibited many unique material properties including very high thermal conductivity. Strong sp 2 bonding configurations in carbon network and nearly perfect self-supporting atomic structure in nanotubes give unusually high phonon-dominated thermal conductivity along the tube axis, possibly even surpassing that of other carbon-based materials such as diamond and graphite (in plane). In this chapter, we explore theoretical and experimental investigations for the thermal-transport properties of these materials.
3,011 citations
"Estimation of the physical properti..." refers background in this paper
...The theoretical thermal conductivity of SWCNTs is usually reported as 6000 W m−1 K−1 at room temperature [6], which is approximately three times the thermal conductivity of diamond, and approximately 104 times that of most polymers [7]....
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