A rational reduced model for elastic layers and its application in pattern formation analysis

微米和亚微米尺度的应力诱导起皱图案具有越来越多的应用，从细胞图案化、光学栅格、创建具有期望的润湿和粘合性能的表面到基于屈曲的测量。尽管近几十年来已经取得了很大的进展，但由于控制方程的复杂性，对模式形成机制的深入理解一直受到阻碍。这一建议旨在打破薄膜-衬底双层中图案形成的数学模型的瓶颈。我们将在非线性弹性和Stroh形式主义的框架下推导出一个合理的简化模型，该模型以自洽的方式结合了非线性、各向异性和预拉伸。新模型的威力将通过分析倍增的二次分叉和脊形成来说明，这些已经被大量研究但尚未完全理解。

Stress-induced wrinkling patterns at micro- and sub-micro-scales have a growing variety of applications ranging from cell patterning, optical gratings, creation of surfaces with desired wetting and adhesion properties, to buckling-based metrology. Although much progress has been made in recent decades, a deeper understanding of the pattern formation mechanisms has been hampered by the complexity of the governing equations. This proposal aims tobreak a bottleneck in the mathematical modelling of pattern formation in film-substrate bilayers. We will derive a rational reduced model for the film behaviour under the frameworks of nonlinear elasticity and Stroh formalism that incorporates nonlinearity, anisotropy, and pre-stretch in a self-consistent manner. The power of the new model will be illustrated by analysing period-doubling secondary bifurcation and ridge formation that have been much studied but not yet fully understood.