Analytical Solutions for Effective Transverse Mechanical Properties and Performance of Radially Loaded Nanotube Based Nanocomposites

It is frequently reported that carbon nanotubes (CNTs) can be filled with various materials in different states to create nanocomposites. These nanocomposite tubes are often incorporated in another host material for further reinforcement to attain properties enhancements. The objective of this paper is to introduce exact analytical close form solutions for the prediction of effective transverse Young’s modulus and Poisson ratio of a matrix-filled nanotube (i.e., a representative element of nanotube reinforced nanocomposites) as well as its mechanical behavior (i.e., displacements, strains and stress distributions) when it is subjected to externally applied uniform radial pressure. In this work, both the nanotube and its filler material are considered to be generally cylindrical orthotropic. For no loss of generality, no plain strain condition is used and axial strain is also taken into consideration to obtain a more precise set of solutions. Analytical formulae are developed based on the principles of linear elasticity and continuum mechanics and then exact solutions are obtained for displacements, strains and stress distributions within the domain of each individual constituent. To validate and verify the accuracy of the closed form solutions obtained from the analytical approach, a 3-D model of a matrix-filled CNT is generated and solved for displacements, strains and stresses numerically, using finite element method. Excellent agreements were achieved between the results obtained from the analytical and numerical methods verifying the analytically obtained exact solutions.