For decades, scientists and researchers believed that two-dimensional (2D) crystals are thermodynamically unstable. Graphene was the first two dimensional material that has successfully been exfoliated from bulk graphite in 2004. We derive interatomic potentials for Graphene for two dimensional lattice structure and using Quasi-harmonic approximations, Mechanical Properties of monolayer Graphene were investigated. The compressibility, hardness, ductility, toughness, brittleness and bonding nature of the Graphene are too well connected with the SOECs. Thus, comprehensive studies on elastic properties are important to show the potential of Graphene in engineering applications. Present studies of monolayer Graphene have been carried out to investigate the elastic constants such as Young’s modulus, Poisson’s ratio, bulk modulus and shear modulus. With the help of elastic constants, the values longitudinal and transverse sound velocities have been computed. We, at present also find the phonon group velocities at Г points along symmetry directions by PYTHON Program. Mechanical Properties were calculated by PYTHON program is agreed very close with the result of other researchers.

Quasi-Harmonic Approximations, Hamiltonian Mechanics, Elastic Constants, Graphene

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