Elastic instability of bilayer graphene using atomistic finite element

In-plane elastic instability of bilayer graphene sheets is investigated using atomistic finite element approaches. The equivalent homogenised properties of graphene sheet are expressed in terms of the thickness, equilibrium lengths and force-field models used to represent the C–C bonds of the graphene lattice. The covalent bonds are represented as structural beams with stretching, bending, torsional and shear deformation, and the strain energies associated to affine deformation mechanisms. The overall mechanical properties and geometric configurations of the nano-structures represented as truss assemblies are then calculated minimising the total potential energy associated to the loading, thickness and average equilibrium lengths of the bonds. Different boundary conditions and aspect ratios are considered for both bilayer and single-layer graphene sheets. The bilayer graphene sheets are found to be offering remarkably higher buckling strengths as compared to single-layer sheets.