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

弹性层合理简化模型及其在图案形成分析中的应用

• 批准号: EP/W007150/1
• 负责人: Yibin Fu
• 金额: $ 6.67万
• 依托单位: Keele University
• 依托单位国家: 英国
• 项目类别: Research Grant
• 财政年份: 2022
• 资助国家: 英国
• 起止时间: 2022 至 无数据
• 项目状态: 未结题
• 来源: https://gtr.ukri.org/projects?ref=EP%2FW007150%2F1
• 关键词: rational; reduced; model; elastic; layers

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.

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。这一建议旨在突破薄膜-基底双层膜中图案形成的数学模型中的瓶颈。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。

项目成果

A one-dimensional model for axisymmetric deformations of an inflated hyperelastic tube of finite wall thickness

• DOI: 10.1016/j.jmps.2023.105276
• 发表时间: 2023-01
• 期刊: Journal of the Mechanics and Physics of Solids
• 影响因子: 5.3
• 作者: Xiang Yu;Yibin Fu

Axisymmetric necking of a circular electrodes-coated dielectric membrane

• DOI: 10.1016/j.mechmat.2023.104645
• 发表时间: 2023-01
• 期刊: Mechanics of Materials
• 影响因子: 3.9
• 作者: Yibin Fu;Xiang Yu

New mountain ridge modes in a film/substrate bilayer

• DOI: 10.1177/10812865231208414
• 发表时间: 2023-11
• 期刊: Mathematics and Mechanics of Solids
• 影响因子: 2.6
• 作者: Yuxin Fu;Yuesheng Wang;Yibin Fu

On the incremental equations in surface elasticity

• DOI: 10.1177/10812865231226183
• 发表时间: 2023-08
• 期刊: Mathematics and Mechanics of Solids
• 影响因子: 2.6
• 作者: Xiang Yu;Yibin Fu