Controlled Wrinkling Analysis of Buckled Thin Films on Gradient Elastic Substrate System: A Numerical Study

Continuous change in wrinkle patterns process of thin films to a gradient substrate is the most challenging problem regarding applying reliable and robust numerical methods for postbuckling analysis film/substrate system. For example, finite element method, simulation suffers from convergence issue, while, spectral methods, it very difficult capture localized behavior soft matters when boundary conditions are complex. When film compressed, can form certain amount wavelength compression exceeds critical value. The compressed compliant system translates sinusoidal wrinkles then period-doubling wrinkling after further compression. In this work, we investigate mathematical model arising changing nature postbuckled using efficient algorithm based on method evolve patterns. We consider substrates three typical variations modulus, namely, symmetry, exponential, power-law model. It has been observed that stable equilibrium path two bifurcation points. At first point, buckling instability occurs, while occurs at second point. material gradients various types, amplitude obtained. This study may help better understanding formation which could be useful designing stretchable flexible electronic devices systems avoid resonance noise environment.