The close-form expressions of the Young's moduli and the fracture stresses of cyclicgraphene, graphyne and supergraphene along their armchair and zigzag directions are derived based on a molecular mechanics model. Checking against present finite-element calculations of their Young's moduli shows that the explicit solutions are reasonable. The obtained analytical solutions should be of great help for understanding the mechanical properties of the graphene-like materials.
Keywords: Young's modulus; carbon allotropes; finite-element method; molecular mechanics model.