An improved molecular structure mechanics method and its application for graphene wrinkling

This paper proposes an improved molecular structure mechanics (iMSM) method to study the wrinkling characteristics of annular graphene sheet (AGS). An idea of variable cross-section beam, combined with 3-node Timoshenko beam, is introduced in the iMSM model for considering the flexibility of C-C bond and C-C joint simultaneously, and the stiffness matrix of beam element is deduced for later calculation. The parameters of equivalent beam are obtained by using an interior point optimization approach. Based on the proposed iMSM model, the wrinkling characteristics of AGS are simulated, which are verified by molecular dynamic (MD) simulation. A predicted model is used to evaluate the wrinkling level of AGS, which agrees well with the iMSM simulation, and then the effects of beam parameters on graphene wrinkling are also analyzed. The results indicate that our proposed model is reliable to the wrinkling analysis of AGS and may be further used for other researches on graphene.