Generally cylindrical orthotropic constitutive modeling of matrix-filled carbon nanotubes: Transverse mechanical properties and responses

The main objective of this article is to introduce exact analytical closed-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-based nanocomposites), as well as its mechanical behavior, when subjected to external loads. In this work, both the nanotube and its filler were considered to be generally cylindrical orthotropic. To ensure no loss of generality, the no plane strain condition was used, and the axial strain was taken into consideration to obtain a more precise set of solutions. Analytical formulae were developed based on the well-established principles of linear elasticity and continuum mechanics, considering effective orthotropic properties for both constituents as continuum tubes. To validate and verify the accuracy of the closed-form solutions obtained from the analytical approach, a three-dimensional finite element analysis was performed, and results were compared to those obtained from the analytical exact solutions. Excellent agreement was achieved, and the analytically obtained solutions were verified.