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Influence of partial blistering on the global and the local stress and couple stress field for a monolayer graphene resting on substrate

Partial delamination of a thin film attached on a substrate is a phenomenon which is likely to occur in many film/substrate systems. Such a delamination strongly affects the developed stress and couple stress field of the film. The objective of this work is to accurately determine the effect of delamination on the stress and the couple stress field of a monolayer-thick graphene film bonded on a polymeric substrate. The theoretical framework we adopt is restricted to the materially and geometrically linear case; graphene is modeled as a hexagonal 2-lattice, while the substrate is assumed to behave in an isotropic linearly elastic manner. The present approach expands significantly on recent findings [4] for the case of partial blistering of the film resting on a substrate. We investigate the influence of the perfect bonding parameter, the substrate material and the size of the specimen, on stresses and couple stresses. Various stress and couple stress profiles illustrate the effect of the above on the local stress and couple stress fields. We also explore the effect on the global stress and global couple stress measures that we define by integrating the local stress and couple stress field along the surface of the film. Selected diagrams illustrate the effect delamination has on these global measures. Our theoretical analysis shows that the effect of delamination is of cardinal importance for the developed stress and couple stress fields of monolayer graphene.