Strength of graphene in biaxial tension

A simple analytical study of a single-atom-thick sheet of graphene under biaxial tension is presented. It is based on the combination of the approaches of continuum and molecular mechanics. On the molecular level the Tersoff-Brenner potential with a modified cut-off function is used as an example. Transition to a continuum description is achieved by employing the Cauchy–Born rule. In this analysis the graphene sheet is considered as a crystal composed of two simple Bravais lattices and the mutual atomic relaxation between these lattices is taken into account. Following this approach a critical failure surface is produced for strains in biaxial tension. The adopted methodology is discussed in the context of the alternative approaches.