Coupled molecular dynamics and micromechanics study of planar elastic properties of graphene with void defects

In this paper, we employ both molecular dynamics (MD) and micromechanics approach to analyze the influence of void defects on the overall 2-dimensional (2D) elastic behavior of graphene. In the micromechanics model (MM), the edge boundary is assumed to have distinct longitudinal elastic stiffness property (Gurtin-Murdoch model) which can be identified by MD simulations of pristine graphene sheet. Both the Finite Element Method (FEM) and MD are used to study the Eshelby problem involving polygonal nanovoids periodically embedded in a graphene sheet. To characterize the heterogeneity effect due to a single nanovoid, we propose to use MD to compute the tensor C which is the first order expansion of the effective tensor C with respect to volume fraction f, related to the dilute scheme estimate. It is shown that the MM performs well for voids with large edges and predicts results consistent with the properties of edge structures. However, MM fails for small voids with short edges where the discrepancies are due to the corner effect which can not be accounted for in MM.