Continuum Models of Carbon Nanotube-Based Composites Using the Boundary Element Method

Abstract

This paper presents some recent advances in the boundary element method (BEM) for the analysis of carbon nanotube (CNT)-based composites. Carbon nanotubes, formed conceptually by rolling thin graphite sheets, have been found to be extremely stiff, strong and resilient, and therefore may be ideal for reinforcing composite materials. However, the thin cylindrical shape of the CNTs presents great challenges to any computational method when these thin shell-like CNTs are embedded in a matrix material. The BEM, based on exactly the same boundary integral equation (BIE) formulation developed by Rizzo some forty years ago, turns out to be an ideal numerical tool for such simulations using continuum mechanics. Modeling issues regarding model selections, representative volume elements, interface conditions and others, will be discussed in this paper. Methods for dealing with nearly-singular integrals which arise in the BEM analysis of thin or layered materials and are crucial for the accuracy of such analyses will be reviewed. Numerical examples using the BEM and compared with the finite element method (FEM) will be presented to demonstrate the efficiency and accuracy of the BEM in analyzing the CNT-reinforced composites.

Potencialidades computacionales del Método de los Elementos Finitos para la modelación y simulación de materiales compuestos: revisión

“…Al estudio que se ha venido realizando utilizando MEF en materiales compuestos reforzados por partí-culas y fibras, se ha sumado el análisis de nanotubos de carbono [44][45][46]. En la Figura 9a, se aprecia un ejemplo del modelado de nanotubos de carbono, donde cada enlace C-C se toma como un elemento tipo "beam", mientras que los átomos de carbono se modelan como nodos.…”

Microstructure-Based Computational Modeling of Mechanical Behavior of Polymer Micro/Nano Composites

“…The geometrical and material parameters for creating and analyzing these RVEs are stated in Table 8.1 (Gade, 2005). In almost all the RVEs generated by other researchers (Griebel and Hamaekers, 2004;Liu et al, 2005;Liu and Chen, 2007;Odegard et al, 2003) in the field of CNT/polymer nano-composites the long CNTs have been inserted in a matrix from one end to the other end in the longitudinal direction. But here for the first time, curved CNTs are studied to observe how their curvatures affect the overall performance of a composite.…”

“…Table 8.4 gives the matrix parameters, and the CNT parameters are the same as presented in Table 8.1. In the study conducted by Gade (2005) and Liu and Chen (2007), very short CNTs were also considered, which are re-simulated in this work just to understand the FEM capabilities range for analyzing that scale. For this purpose, one RVE model containing a short hollow CNT with end caps is constructed here (see Fig.…”

A continuum model for carbon nanotube-infused polyimides

“…The first focuses on the molecular level. Molecular models use simulations to determine local interactions among atoms or chemical reactions between the matrix and nanotubes [5,9,10,11]. Molecular models are limited to very small systems due to the high computational cost.…”