A membrane theory for circular graphene sheets, based on a hyperelastic material model for large deformations

Large deflections relevant for suspended circular graphene sheets with simply supported boundaries are computed by a theory for 2D membranes subjected to several types of vertical axisymmetric forces, based on the principle of virtual power (PVP). Corresponding stress-strain relations are provided in the form of a nonlinear hyperelastic material model for graphene. When approximating the deflections through Fourier series, the PVP yields a nonlinear algebraic system of equations, which is solved by the iterative Newton-Raphson procedure. The new computational efficient method is validated through comparison of the numerical results it provides, with predictions obtained from experimental nanoindentaion measurements.

Automated summary

This study computes large deflections of suspended circular graphene sheets with simply supported boundaries under various types of vertical axisymmetric forces based on the principle of virtual power. The deflections are approximated using a Fourier series, resulting in a nonlinear algebraic system of equations solved by an iterative Newton-Raphson procedure. The method is validated using experimental nanoindentation measurements.