Instability driven surface patterns: Insights from direct three-dimensional finite element simulations

Abstract

Surface patterns driven by mechanical instability commonly form in thin-film structures with a compliant substrate. In this study a practical three-dimensional (3D) finite element modeling approach is employed to directly simulate surface instabilities. It is based on our previously developed embedded imperfection technique in two-dimensions, and is now successfully implemented in 3D to capture sinusoidal wrinkling under uniaxial compression and the checkerboard pattern under equi-biaxial compression. The numerical approach overcomes typical challenges in computationally modeling thin-film buckling instability without the need of sophisticated treatment. The simulation results show that instability-controlled surface patterning is not an instantaneous process. A local disturbance in deformation originates from the imperfection site and propagates outward, eventually leading to a uniform pattern across the entire surface.