薄膜结构屈曲褶皱现象的多尺度建模与仿真

The central aim of this project is to develop advanced multi-scale modelling and simulation techniques and methodologies to study the buckling and wrinkling phenomena of membranes. It's well known that compressive stresses can cause the appearance of local wrinkling. Often the modal wavelength is small as compared with the size of the structure. Direct simulation of these instabilities is not the best option for the following reasons: i) it's difficult to pilot the nonlinear simulation because too many solution paths exist around the useful one, and ii) direct simulation requires a large amount of elements and this leads to a high computational complexity. Thus, there is a need for accurate and computationally efficient techniques that take into account the most important scales involved in the simulation and make it easy to attend the useful solutions. Toward this end, two primary models will be developed and coupled in this study: the microscopic model and the macroscopic model. The latter will be developed by a new technique of slowly variable Fourier coefficients with the aim of describing the influence of local wrinkling on structure behaviour. As usual in model reduction, it is not obvious that the macroscopic model holds good up to the boundaries. In order to accurately capture the boundary effects, the microscopic model will be used in the boundary layers when it is necessary. The microscopic model and macroscopic model will be coupled by a bridging domain technique (Arlequin method), which permits to glue different mechanical models by using Lagrange multipliers in the coupling zone. The coupled nonlinear systems will be solved by an efficient technique, the Asymptotic Numerical Method, which is more reliable and less time consuming than other iterative classical methods, such as the modified Newton method and the Newton-Raphson method. To validate the proposed multi-scale methods, an experimental platform that makes loading in two perpendicular axes on membranes will be designed and constructed to analyze the wrinkling phenomena of metallic membranes. The results of this project are hoped to accurately and efficiently predict and prevent membrane wrinkling, and also to help to study the other instability phenomena with nearly periodic patterns.

薄膜结构的屈曲褶皱现象广泛存在于工程技术领域中，寻求其快速准确的建模与仿真方法，探知其关键影响因素，对预测及预防该类现象有重要的科学意义。项目旨在综合运用慢变傅立叶系数法、桥域多尺度方法及数值渐近法，提出一套兼顾计算效率与精度的多尺度建模与仿真方法。其中，应用在结构大部分区域的宏观模型由慢变傅立叶系数法建立，其在提高计算效率的同时能够通过选择失稳模态控制非线性求解路径，而应用在边界处的细观模型则用来精确描述边界效应。宏细观力学模型的耦合通过桥域多尺度方法实现。建立起来的多尺度强非线性系统由具有收敛速度快、计算精度高等特点的数值渐近法求解。同时，项目将试制双轴加载实验装置，采用非接触式三维全场变形测量系统，完成对金属薄膜失稳现象的实验研究，以验证上述数值方法。项目成果以期为快速预测薄膜失稳及研发合理的预防措施提供理论支持与技术工具，并为其它具有周期性变化特性的失稳问题研究打下坚实的科学基础。

薄膜结构的屈曲褶皱现象广泛存在于工程技术领域中，探知其关键影响因素， 寻求其快速准确的建模与仿真方法，对预测及预防该类现象有重要的科学意义。项目综合运用了慢变傅立叶系数法、桥域多尺度方法及数值渐近法，开发了一套兼顾计算效率与精度的多尺度建模与仿真方法。其中，应用在结构大部分区域的宏观模型由慢变傅立叶系数法建立，其在提高计算效率的同时能够通过选择失稳模态控制非线性求解路径，而应用在边界处的细观模型则用来精确描述边界效应。宏细观力学模型的耦合通过桥域多尺度方法实现。建立起来的多尺度非线性系统由具有收敛速度快、计算精度高等特点的数值渐近法求解。同时，项目试制了双轴加载实验装置，采用非接触式三维全场变形测量系统，开展了对金属薄膜失稳现象的实验研究。.本项目通过构建傅立叶包络线模型丰富了双尺度渐近理论，通过缩减耦合优化了跨尺度关联方法，通过多尺度建模实现了薄膜失稳的高效数值仿真，通过无量纲分析揭示了薄膜失稳的相关机理，并确立了一个影响薄膜失稳的关键参数，通过实验研究部分验证了数值仿真的可靠性，从而为快速预测薄膜失稳及研发合理的预防措施提供理论支持与技术工具。在以上研究成果的基础上，本项目将研究内容扩展至其它两种空间上具有近似周期性变化的失稳问题研究：薄膜/衬底系统的微观褶皱以及夹层结构整体失稳与局部褶皱现象。研究成果显示，本项目提出的多尺度建模与仿真方案在保证计算精度的同时能够大幅提高上述各类问题的计算效率。