Auxeticity in Single Layer Graphene Sheets

In this work we identify boundary conditions and types of loading for single layer graphene sheets (SLGS) suggesting an auxetic behaviour for the C-C bonds and the graphene layers. The mechanical properties of the SLGS are identified using an equivalent atomistic-continuum model proposed in [1], and compared with existing data in open literature. Under clamped-free uniaxial loading, the overall mechanical properties of the SLGS can be explained assuming an equivalent mechanical auxetic behaviour of the C-C bonds. When the SLGS have full blocked boundary conditions and undergo resonance, the minimisation of the Hamiltonian leads to the identification of equivalent negative Poisson’s ratio (NPR) in the graphene sheets.