Principal Investigators: Hamid Bellout and Frederick Bloom Department of Mathematical Sciences Northern Illinois University DeKalb, IL 60115
This proposal was received in response to Nanoscale and Engineering Initiative NSF 03-043, Category NER
Using molecular dynamics simulations at the atomic scale, the principal investigators construct a mathematical model for the constitutive behavior of a graphitic sheet; this is accomplished by applying homogenization theory to a hexagonal array of carbon atoms with a specific chirality vector. The molecular dynamics simulations generate a set of periodic, rapidly varying, elastic constants for the graphitic sheet which incorporate the previously ignored torsional component of strain. The analysis is then extended to specific arrays of carbon atoms on the surface of a single-walled nanotube of the same chirality with the goal of determining the deformation which takes the graphitic sheet, modeled as a continuum, onto the nanotube surface. The derived effective constitutive relations for single-walled nanotubes allows for the computation of an effective thickness for nanotube shells and for an extension of the modeling effort to multiwalled nanotubes. In particular, the research leads to new results concerning the compressive buckling of single-walled and multi-walled carbon nanotubes and predictions of their ultimate strength in nanotube composites; it also obviates the need for an expanding array of expensive and time-consuming molecular dynamics studies.
Considerable interest has been generated in nano-structured non-metallic materials because of their potential for providing significant improvements in both mechanical and physical properties with respect to traditional structural materials. Carbon nanotubes, in particular, are believed to possess a strength which is unmatched by any other known material and composite materials based on carbon nanotubes have the potential of providing strength-to-weight ratios exceeding those of any materials currently available. Because small fiber composites are relatively easy to process, the mechanical properties of carbon nanotubes make them outstanding candidates for the fabrication of the optimal carbon fiber reinforced materials. The present research effort is geared towards the development of theories for predicting the mechanical properties of individual nanotubes; such knowledge is a prerequisite for understanding the bulk mechanical properties of nanotube-polymer composites in terms of the molecular structure of the polymer, the nanotubes, and the polymer/nanotube interfaces. Nanotube reinforced polymer composites are already being thought of as the ideal structural materials of the future for applications which range from advanced components for the next generation of civilian, military, and space vehicles and aircraft to protective uniforms for members of the armed forces.
