Investigation of buckling of double-walled carbon nanotubes embedded in an elastic medium using the energy method

Elastic buckling of a long double-walled carbon nanotube embedded in an elastic medium and subjected to a far-field hydrostatic pressure is analyzed using the energy method. The study is on the basis of elastic-shell models at nano-scale, and the effect of van der Waals forces on the buckling is considered. The double-walled carbon nanotube is assumed to be thin and the tube is taken to be perfectly bonded to the surrounding medium. Both normal and shear stresses at the outer tube-medium interface are included. The difference between the Poissonʹs ratio of the tube and that of the elastic medium is taken into account. An expression is derived relating the external pressure to the buckling mode number, from which the critical pressure can be obtained. As a result, the critical pressure is dependent on the inner radius-to-thickness ratio, the material parameters of the elastic medium, and the van der Waals force.