2007 NSTI Nanotechnology Conference and Trade Show - Nanotech 2007 - 10th Annual

Closed form Exact Analytical Solutions for Effective Mechanical Properties and Responses for Nanotube Reinforced Nanocomposites

D. Askari and M. Ghasemi-Nejhad
University of Hawaii at Manoa, US

Keywords:
carbon nanotube, nanocomposite, three-phase composite cylinder, generally cylindrical orthotropic, effective mechanical properties and responses, analytical analysis, finite element analysis

Abstract:
In this paper, analytical and numerical approaches are employed to investigate the effective axial mechanical properties and mechanical behavior of a three-phase composite cylindrical model, representing a unit cell for a polymer nanocomposite reinforced by a matrix-filled nanotube, and subjected to an axial load. Generally cylindrical orthotropic properties are considered for all three constituents. First, basic elasticity equations in a cylindrical coordinate system for orthotropic materials are used to derive the governing equation. Solution to the governing equation provides the displacement solutions in terms of materials properties, geometrical dimensions, and five unknown constants. The substitution of the displacements into the strain equations and then results into the constitutive equations yields the stress equations. Next, the interface and boundary conditions are applied to obtain the five unknown constant coefficients. Using the basic definitions for total axially applied load and the effective mechanical properties, closed form exact analytical solutions are obtained for the effective longitudinal Young’s modulus and major Poisson’s ratio, as well as the displacements, strains, and stresses distributions within the domain of each constituent. To verify the exact analytical solutions, finite element analysis is performed and the results are compared with the analytical solutions where excellent agreements are achieved

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