# Calculation of Elastic Modulus of Graphene in LAMMPS

Hello everyone, I want to calculate elastic constants (C11, C22, C12, and C66) for a single layer graphene sheet by MD simulation in LAMMPS. I am using the following equation:

E = (C11*C22-C12*C21)/C22 and poisson ratio = C12/C22 from this paper:

My strain in y and z direction is zero. I calculated sigma11, and sigma22 and tau12 in x, y and xy direction from LAMMPS by compute stress/atom command. The equations to solve from the stress-strain relationship would be:

sigma11 = C11*epsilon11 + C22*epsilon22

sigma22 = C12*epsilon11 + C22*epsilon22

tau12 = C66*gamma12

But as, epsilon22 = 0, sigma reduces to sigma11 = C11*epsilon11 and from this equation we can calculate C11.

My question is, what is the actual value of sigma11 and epsilon11 to be used here. If they are fracture stress and strain, then my C11 = 170 GPa. If, I take very low values of strain, for example 0.04, then C11 = 700 GPa. But it should be 977 Gpa as the paper says.

Am I understanding the calculation correctly? I can share my LAMMPS input file if required.

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