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

在微米和亚微米尺度下的应力诱导的弯曲图案具有越来越多的应用，从单元图案化、光栅、具有期望的润湿和粘附特性的表面的创建到基于弯曲的计量。虽然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，对图案形成机制的更深入理解一直受到阻碍。该提案旨在打破薄膜-基底双层中图案形成数学建模的瓶颈。我们将推导出一个合理的简化模型的非线性弹性和斯特罗形式主义，结合非线性，各向异性，并在一个自洽的方式预拉伸的框架下的膜行为。新模型的力量将通过分析倍周期二次分叉和脊的形成，已被大量研究，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.