Equivalent elastic moduli of a zigzag single-walled carbon nanotube given by uniform radial deformation

Under hydrostatic pressure, the equivalent elastic moduli of a zigzag single-walled carbon nanotube (SWNT) are analytically determined by energy conservation, with the consideration of the covalent bond deformation. The theoretical predictions on the transverse mechanical properties of a zigzag SWNT agree reasonably well with those given by the molecular structures mechanics simulations and also the ab initio calculations. From the simple geometry calculation, the circumferential strain is about 2–3 times of the axial strain of a zigzag SWNT under hydrostatic pressure. The bulk modulus of a zigzag SWNT is found to be 3/7 times of its radial Young's modulus.