Effective Young's Modulus of Carbon Nanotube Composites: From Multi-Scale Finite Element Predictions to an Analytical Rule

This paper presents a modification of rule of mixtures that is able to take into account the interfacial effects between the reinforcement consisting from single-walled carbon nanotubes and the matrix, in order to predict the effective Young's modulus of the nanocomposite. Based on the micromechanical theory, a semi-continuum finite element model is employed to perform numerical experiments. More specifically, a composite material which is uniformly reinforced with continuous and well aligned single walled carbon nanotubes is under consideration. A cylindrical representative volume element which contains a single walled carbon nanotube is analyzed using the finite element method. The reinforcement is modeled, via a technique proposed by the authors, in accordance with its atomistic microstructure. Spring-based line elements are employed to simulate the discrete geometrical structure and the molecular mechanics behavior of the nanotube. On the other hand, the matrix is modeled as a continuum medium by utilizing solid elements. Due to the difficulty in simulating the complicated effects that take place along the interfacial zone, for first time in literature of nanocomposites, the interfacial region is simulated via the use of special joint elements of variable stiffness which interconnect the two materials. Parametric studies are conducted and the numerical fitting of results yields a novel modified rule of mixtures.