Elastic deformation behavior of freestanding MoS2 films using a continuum approach

In this paper, an approximate solution based on the continuum mechanics is presented to obtain the mechanical response of freestanding single and two layers molybdenum disulfide (MoS2) films. Both circular and rectangular geometries as well as point load and uniform pressure are investigated. The partial differential equilibrium equations are established based on the non-linear Föppl membrane theory for both circular and rectangular films. The Galerkin method is then employed to solve the non-linear partial differential equilibrium equations in case of circular films. Also, the principle of virtual work affords another means of obtaining an approximate solution for rectangular film. Theoretical predictions for the width of membrane regions enable us to estimate the analytical deflection and stress distributions. Finally, the obtained results are compared to the available experimental and theoretical results and a good agreement is seen. It can be concluded that the continuum approach can be used to study the behavior of the MoS2 films.