Application of equivalent cylindrical inhomogeneity to modeling of CNT and analysis of influence of CNT distributions on response of functionally graded structural elements

Abstract

A mathematical model based on the concept of the energy-equivalent inhomogeneity combined with the method of conditional moments (MCM) has been applied to analyze Carbon Nanotube (CNT)-reinforced materials. The idea of the energy-equivalent inhomogeneity is to replace the inhomogeneity and its interphase by a single equivalent inhomogeneity. It is evaluated for cylindrical inhomogeneity with Gurtin-Murdoch surface model and spring layer model of interphases. Inclusion of multiple mechanisms in the description of interphases is applied to the CNT-reinforced materials. The CNT is modeled as a cylindrical high-stiffness surface. A weak zone surrounding the CNT can be modeled by a spring layer. In this case, one Gurtin-Murdoch and one spring layer models would need to be combined. To evaluate the effective properties of CNT-reinforced materials a statistical method, the MCM, has been employed which describes random distribution of CNT’s. Closed-form formulas for the components of the effective stiffness tensor of such composites have been developed. A composite plate weakened by a hole under different types of loading is considered. It is assumed, that the plate made of the polymer with randomly distributed and disoriented CNT’s. Analysis of how various special distributions of CNT concentration affect the response of this plate is performed.