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.

由机械不稳定性驱动的表面图案通常在具有顺应性基板的薄膜结构中形成。在这项研究中，采用了实用的三维（3D）有限元建模方法来直接模拟表面不稳定性。它基于我们先前开发的二维嵌入式缺陷技术，现已成功以3D方式实现，以捕获单轴压缩下的正弦皱纹和等双轴压缩下的棋盘格图案。数值方法克服了在无需复杂处理的情况下对薄膜屈曲不稳定性进行计算建模的典型挑战。仿真结果表明，不稳定性控制的表面构图不是一个瞬时过程。