A validated energy approach for the post-buckling design of micro-fabricated thin film devices

摘要

The buckling of an elastic thin film is studied in the light of an energy minimization method. Specifically, a comprehensive treatment of the Rayleigh-Ritz method is presented. Detailed mechanical modelling, analytical and numerical derivation of stability criteria, physical interpretation of buckling shapes, numerical code implementation, and experimental validations of selected simulations are addressed. The thin film deflection is prescribed as a superposition of buckle functions to provide displacement field parameterizations involving trigonometric functions. An energy minimization procedure is applied to calculate the unknown coefficients to predict the buckling shape and amplitude. Critical buckling values representing the thresholds for instability transitions in the system are calculated from the eigenvalues of the Hessian of the potential energy. Comparison between simulation results and experimental measurements show the great potential of this method to predict thin film buckling. The validated model is exploited by derivation of a new design space for thin film fabrication where the post-buckling mechanics is controlled.