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This paper elucidates the global and local interactive buckling behavior of a stiff film resting on a compliant substrate under uniaxial compression. The resulting governing non-linear equations (non-autonomous fourth-order ordinary differential nonlinear equations with integral conditions) are then solved by introducing a continuation algorithm, which offers considerable advantages to detect multiple bifurcations and trace a complex post-buckling path. The critical conditions for local and global buckling and respective post-buckling equilibrium paths are carefully studied. Two different evolution mechanisms of buckling modes and processes from destabilization to restabilization (snap-back) are observed beyond the onset of the primary sinusoidal wrinkling mode in the post-buckling range. In addition, the shear modulus of an orthotropic substrate acts as a dominant role in the bifurcation portrait. Our results offer better understanding of the global and local buckling behaviors of such a bilayer system, and can open up new opportunities for the design and applications of novel nanoelectronics. [ABSTRACT FROM AUTHOR]

Abstract: A pseudo beam model with 3-node beam element is proposed to simulate the modal behavior of the wrinkled single-layered graphene sheets (SLGS) based on molecular structural mechanics (MSM) method. The wrinkling characteristics are simulated using a direct perturbed-force technique originated from the continuum theory. The primary bifurcation and the secondary wrinkling behaviors are investigated so as to obtain the characteristics of the formation and the evolution of the wrinkles. The wrinkled shape, stress and effective mass are introduced into the modal model using the updated geometry technique. The effects of the wrinkles on the vibration characteristics of the SLGS are then interpreted by comparing with the unwrinkled case. The effects of the aspect ratio on the modal behavior of wrinkled SLGS are further studied. Based on the MSM simulation results and the continuum thin plate model, a prediction model is proposed to obtain the natural frequency of wrinkled SLGS. The predictions agree well with the MSM simulations. The results and observations are good references to design a wrinkled highly frequency nano-devices. [Copyright &y& Elsevier]