Ripples and cracks in graphene

textGraphene is a single layer two-dimensional honeycomb lattice of carbon atoms. It is one of the toughest, lightest, and most conductive materials known. Graphene was first isolated using adhesive tape in 2004, and awarded the Physics Nobel Prize in 2010. Here we focus on the mechanical properties of graphene. First we present an analytical study, together with numerical simulations, of ripples in graphene. We show that ripples observed in free-standing graphene sheets can be a consequence of adsorbed OH molecules sitting on random sites. The adsorbates cause the bonds between carbon atoms to lengthen slightly. In the second part of this work we study the fracture mechanics of graphene. Experiments on free-standing graphene can expose the graphene sheets to out-of-plane forces. Here we show that out-of-plane forces can cause free-standing graphene to fracture. This fracture mode is known as the tearing mode and is common in materials such as paper. We present a numerical study of the propagation of cracks in clamped, free-standing graphene as a function of the out-of-plane force. We also obtain an analytical expression for the minimum force required to tear a two dimensional sheet, which is our model of graphene, in terms of the initial crack length.Physic