Mechanical effects of self-stress states in graphene membranes in multiscale modeling

Graphene, an atomically thin material renowned for its exceptional properties, plays a pivotal role in several technological applications. This work elucidates critical aspects of graphene research, particularly focusing on the effects of its transfer onto suitable substrates. Indeed, from the mechanical point of view the transfer process induces self-stresses within the graphene layer. In addition, formidable applications in the field of biosensors, filtration membranes, and special electronic devices are based on precision perforated-graphene. However, perforation introduces localized stress concentrations, altering mechanical behavior and the strength of the graphene membrane. In this paper, the effects of self-stress states on graphene membrane strength are studied through numerical models. Specifically, the mechanical strength of pristine and perforated graphene membranes subjected to different self-stress states is studied at the nanoscale, using a static molecular mechanics model. Then, a suitably calibrated hyper-elastic continuum model is formulated and correlated with the molecular mechanics model to study the mechanical strength at the micron scale, which is the actual scale of the membranes. Results give important insights on the effects of self-stress states in graphene membranes. We found out also that the interaction distance between holes is strongly influenced by the self-stress state.