Temperature-dependent multiscale modeling of graphene sheet under finite deformation

The homogenized constitutive models that have been utilized to simulate the behavior of nanostructures are typically based on the Cauchy-Born hypothesis, which seeks the fundamental properties of material via relating atomistic information to an assumed homogeneous deformation field. It is well known that temperature has a profound effect on the validity and size-dependency of the Cauchy-Born hypothesis in finite deformations. In this study, a temperature-related Cauchy-Born formulation is established for graphene sheets and its performance is examined through a direct comparison between the continuum-based constitutive model and molecular dynamics analysis. It is demonstrated that if the temperature increases, the validity surfaces shrink, which is not highly dependent on the size of specimen. At finite strains, graphene sheet exhibits material softening and hardening, which are manifested in the elastic constants. The developed constitutive model is used to study the effect of applied deformations at various temperature levels on the elastic constants of graphene sheets. Finally, a novel multiscale finite element approach is developed for the analysis of graphene sheets in finite strain regime based on the proposed atomistic-continuum model. The method can be used efficiently in the simulation of large specimens where the application of molecular dynamics requires considerable computational efforts. The efficiency and robustness of the proposed multiscale approach are shown through several numerical examples.