A cohesive law for multi-wall carbon nanotubes

We have established the cohesive law for carbon nanotube (CNT) walls in multi-wall CNTs. The interactions between CNT walls are characterized by the van der Waals force. The tensile cohesive strength and cohesive energy are given in terms of the area density of CNT and parameters in the van der Waals force. For an infinitely long CNT, the shear cohesive stress between CNT walls vanishes, and the tensile cohesive stress depends only on the opening displacement. For a finite CNT, the tensile cohesive stress remains the same, but the shear cohesive stress depends on both opening and sliding displacements, i.e. the tension/shear coupling. The simple, analytical expressions of the cohesive law are useful to study the interaction between walls in multi-wall CNTs.