Continuum-molecular modelling of graphene

In the present contribution we address the modeling of graphene membranes using a hierarchical modeling strategy to bridge the scales required to describe and understand the material. Quantum Mechanical (QM) and optimized Molecular Mechanical (MM) models are used to describe details on the nanoscale, while a multiscale continuum mechanical method is used to model the graphene response at the device or micrometer scale. The complete method is obtained on the basis of the Cauchy Born Rule (CBR), where the continuum model is coupled to the atomic field via the CBR and a local discrete fluctuation field. The MM method, often used to model carbon structures, involves the Tersoff--Brenner (TB) potential; however, when applying this potential to graphene with standard parameters one obtains material stress behavior much weaker than experiments. On the other hand, the more fundamental Hartree Fock and Density Functional Theory (DFT) methods are computationally too expensive and very limited in terms of their applicability to model the geometric scale at the device level. In this contribution a simple calibration of some of the TB parameters is proposed in order to reproduce the results obtained from QM calculations. Subsequently, the fine-tuned TB--potential is used for the multiscale modeling of a nano indentation sample, where experimental data are available. Effects of the mechanical response due the calibration are demonstrated.