In the recent past, graphene has emerged as a potential candidate for developing nanocomposites with improved properties [1, 2]. The experimental characterization of graphene/polymer nanocomposites is a challenging process, and hence, computational approaches for predicting the behavior of such materials have also extensively been employed. Various multiscale models are available in the literature for predicting the properties of carbon nanotube (CNT)-based nanocomposites [3–5], but very few models have been presented to study graphene nanocomposites. For example, Cho et al. [6] developed a numerical model in conjunction with Mori-Tanaka approach to study the elastic constants of randomly distributed graphene in polymer. Awasthi and his team [7] investigated the load transfer mechanism between polyethylene and graphene sheets. Montazeri and Tabar [8] developed a finite element (FE)-based multiscale model to investigate the elastic constants of graphene-based nanocomposites.

Buckling in isolated graphene sheets was modeled by several researchers [9–11]. However, buckling stability of graphene/polymer nanocomposites was only reported by Rafiee et al. [12]. Using an experimental and analytical approach, up to 50% and 32% improvement in the buckling stability of nanocomposites was reported respectively. In the analytical approach, an Euler buckling formulation was employed, and elastic properties required in the Euler equation were estimated by experimental means. The discrepancies between the two buckling stabilities were attributed to scaling issues.

It is well established that the reinforcement of polymer with graphene increases the elastic modulus of the material which further improves buckling stability. The aim of this study is to propose a numerical model which can estimate the increase in buckling stability with different volume fractions of graphene and can further be extended to complex shapes and structures.

It has been reported that achieving a uniform dispersion of two-dimensional graphene sheets in polymer is more challenging compared to the mixing of one-dimensional CNT. Moreover, the application of nanocomposites is not limited to simple structures, and the comprehension of material behavior in complex structures is restricted when employing experimental and analytical methods. Consequently, research efforts are increasingly focused on numerical approaches. To overcome some of the limitations that exist in experimental and analytical work, a multiscale representative volume element (RVE) is proposed in this paper to investigate buckling phenomena in graphene/polymer nanocomposites under the assumption that graphene is uniformly distributed in the polymer. To the knowledge of the present authors, no numerical model has been reported yet to study the effect of graphene on the buckling strength of nanocomposites. In the proposed technique, graphene was modeled in the atomistic scale, whereas polymer deformation was analyzed as a continuum.