Graphene is expected to open up a world of new possibilities in the field of micro and nano sensors, due to its outstanding properties. However, graphene membranes suffer from high damping which limit their performance. The physical mechanism behind this damping is still unknown. Therefore, in this work, it is investigated how coupling between eigenmodes due to nonlinear stiffness causes damping. Besides, a method to construct this nonlinear stiffness for reduced order models is improved. Using this, numerical simulations are compared to experimental results for validation.