Eccentric compression stability of multi-walled carbon nanotubes embedded in an elastic matrix

This paper reports the results of an investigation on the eccentric compression stability of multi-walled carbon nanotubes embedded in an elastic matrix. Based on continuum modeling, a multilayer shell model is presented for the eccentric compression buckling of multi-walled carbon nanotubes embedded in an elastic matrix, in which the effect of van der Waals forces between two adjacent tubes is taken into account. The critical bending moment and the eccentric compression mode for three types of multi-walled carbon nanotubes with different layer numbers and ratios of radius to thickness are calculated. Results obtained show that the eccentric compression buckling mode corresponding the critical bending moment is unique, and is different from the purely axial compression buckling of an individual multi-walled carbon nanotube. For different types of multi-walled carbon nanotubes, the effect of matrix stiffness on the critical bending moment of multi-walled carbon nanotubes under eccentric compression loading is obviously different, and is dependent on the innermost radius and layer numbers of the multi-walled carbon nanotubes. The critical bending stress exerted on the center tubes of nearly solid multi-walled carbon nanotubes does not change as the ratio of the axial compression loading to the bending membrane force increases. The new features and meaningful numerical results in this paper are helpful for the application and the design of nanostructures in which multi-walled carbon nanotubes act as basic elements.