Can Raman Shift Be Used to Characterize the Mechanical Property of Graphene?

Graphene has potential in a variety of applications, including strain-engineering electronics and sensors. In the heart of these applications is the strain dependence of electronic properties associated to the strain-induced Raman shift of graphene. In this work, we extend the relationship between the Raman shift of strained graphene and the mechanical strains for uniaxial tension to three-dimensional strain state and analyze the bending-induced Raman shift of orthotropic, monolayer graphene of rectangular and elliptic shapes, respectively, under the action of uniform pressure. The results show that the largest Raman redshift is present at the center of the graphene for both geometric configurations, and there exists Raman blueshift near the edges of the graphene. For both geometrical configurations, the contours of the Raman shift around the center are present in the shape of ellipse, which is dependent on the boundary conditions and geometrical configurations of the graphene. The geometric shape of the contours of the Raman shift likely cannot represent the anisotropic behavior in the mechanical deformation of graphene, and the initial state and constitutive relationship of graphene are needed to characterize the mechanical property of graphene via the strain-induced Raman shift.