Surface instability of compliant film/substrate bilayers has raised considerable interests due to its broad applications such as wrinkle-driven surface renewal and antifouling, shape-morphing for camouflaging skins, and micro/nano-scale surface patterning control. However, it is still a challenge to precisely predict and continuously trace secondary bifurcation transitions in the nonlinear post-buckling region. Here, we develop lattice models to precisely capture the nonlinear morphology evolution with multiple mode transitions that occur in the film/substrate systems. Based on our models, we reveal an intricate post-buckling phenomenon involving successive flat-wrinkle-doubling-quadrupling-fold bifurcations. Pre-stretch and pre-compression of the substrate, as well as bilayer modulus ratio, can alter surface morphology of film/substrate bilayers. With high substrate pre-tension, hierarchical wrinkles emerge in the bilayer with a low modulus ratio, while a wrinkle-to-ridge transition occurs with a high modulus ratio. Besides, with moderate substrate pre-compression, the bilayer eventually evolves into a period-tripling mode. Phase diagrams based on neo-Hookean and Arruda-Boyce constitutions are drawn to characterize the influences of different factors and to provide an overall view of ultimate pattern formation. Fundamental understanding and quantitative prediction of the nonlinear morphological transitions of soft bilayer materials hold potential for multifunctional surface regulation.

顺应性膜/基材双层的表面不稳定性因其广泛的应用而引起了广泛的关注，例如皱纹驱动的表面更新和防污，伪装皮肤的形状变形以及微/纳米级表面图案控制。但是，精确预测并连续跟踪非线性后屈曲区域中的二次分叉转变仍然是一个挑战。在这里，我们开发出晶格模型，以精确捕获膜/衬底系统中发生的多模态转变的非线性形态演变。根据我们的模型，我们揭示了复杂的屈曲后现象，其中涉及连续的平皱加倍四倍折叠分叉。基材的预拉伸和预压缩以及双层模量比可以改变薄膜/基材双层的表面形态。在较高的基材预张力下，双层中的褶皱以低的模数比出现，而皱纹到脊的过渡以高的模数比出现。此外，在适度的底物预压缩下，双层最终演变为周期三倍模式。绘制了基于新Hookean和Arruda-Boyce构造的相图，以表征不同因素的影响并提供最终图案形成的整体视图。对软双层材料的非线性形态转变的基本理解和定量预测具有多功能表面调节的潜力。通过适度的底物预压缩，双层最终演变为三倍周期模式。绘制了基于新Hookean和Arruda-Boyce构造的相图，以表征不同因素的影响并提供最终图案形成的整体视图。对软双层材料的非线性形态转变的基本理解和定量预测具有多功能表面调节的潜力。通过适度的底物预压缩，双层最终演变为三倍周期模式。绘制了基于新Hookean和Arruda-Boyce构造的相图，以表征不同因素的影响并提供最终图案形成的整体视图。对软双层材料的非线性形态转变的基本理解和定量预测具有多功能表面调节的潜力。