Fig. 1. Schematic diagram of the graphene/substrate structure under uniaxial tension.

Fig. 2. The force balance of an element of graphene.

Fig. 3. Analysis of interfacial shear stresses at local interface.

Fig. 4. (a) Two-dimensional nonlinear shear-lag model; (b) bilinear cohesive shear-mode (Ⅱ + Ⅲ) law.

Fig. 5. Distributions of graphene’s normal strains (a) ε_x and (b) ε_y; distributions of interfacial shear stresses (c) τ_zx and (d) τ_zy at the elastic bonding stage (ε_sx = 0.2%).

Fig. 6. Distributions of graphene’s strains (a) ε_x and (b) ε_y; distributions of interfacial shear stresses (c) τ_zx and (d) τ_zy along several representative lines.

Fig. 7. Variation of the critical strain for sliding with the width of graphene at different Poisson's ratio of substrate (the lines are the theoretical results, and the scatter points are the FEM results).

Fig. 8. Schematic diagram of interfacial sliding stage.

Fig. 9. Distributions of graphene’s normal strains (a) ε_x and (b) ε_y; distributions of interfacial shear stresses (c) τ_zx and (d) τ_zy at the interfacial sliding stage (ε_sx = 1%).

Fig. 10. Variation of compressive strain ε_y^Cat the center point C of graphene with its width when the strain of substrate is different.

Fig. 11. Comparisons of the results obtained via one-dimensional and two-dimensional models (W = 21.8 μm): (a) ε_x and (b) τ_zx at the elastic bonding stage (ε_sx = 0.2%); (c) ε_x and (d) τ_zx at the interfacial sliding stage (ε_sx = 1%).

Fig. 12. Comparisons of the results obtained via one-dimensional and two-dimensional models (W = 1 μm): (a) ε_x and (b) τ_zx at the interfacial sliding stage (ε_sx = 1%).

Fig. 13. Fitting results of experimental data by using 2D model: (a) ε_m along the centerline (y = W/2) when the tensile strain ε_sx = 0.25%; (b) at the center point C under different tensile loads.