宏细观失稳交互作用下长纤维复合材料结构的多尺度建模与仿真

Long fiber composites are widely observed in both nature and engineering. It is well known that their compressive failure often initiates from fiber microbuckling. Direct simulation is not the best option because it requires a large number of elements that is very expensive due to the interactive coupling between fiber microbuckling and structural instability. Moreover, it is difficult to pilot the nonlinear calculation since there exist lots of bifurcation points around the useful one. The aim of this project is to develop a computationally efficient yet accurate multiscale model to simulate and analyze the instability phenomena of long fiber composites. Towards this end, the multilevel finite element method (FE2), the Fourier-related approach and the bridging technique will be combined in a complementary way. As a computational homogenization method, the FE2 method is able to realize the real-time information transition between the microscopic and macroscopic scales. Although this method permits to save a lot of degrees of freedom, its computational cost is still expensive, because very fine mesh is needed for each RVE to capture the local buckling with large wavenumbers. To overcome this difficulty, the Fourier-related analysis is carried out on the RVEs, where the microscopic unknowns are expanded into Fourier series, and the new RVE model is based on the Fourier coefficients of the microscopic unknowns, which makes the RVE mesh independent of the wavelength and leads to a considerable reduction of computational cost. However, as usual in model reduction, it is not obvious that the homogenized model holds good up to the stress concentration zones. Therefore, the fine model should be involved in the boundary layers to capture local effects. In order to couple the proposed homogenized model in the bulk and the fine model in the boundary layers, a bridging domain technique is implemented by using Lagrange multipliers as fictive gluing force in the coupling zone. The nonlinear multiscale systems will be solved by an efficient technique, the Asymptotic Numerical Method, in which the bifurcation indicator could be introduced to precisely detect all the bifurcation points and the evolution of the instability patterns. The results of this project are expected to improve the understanding of instability mechanism of long fiber composites and provide an efficient computational platform for accurately predicting and preventing such failure.

长纤维复合材料结构广泛存在于自然界和工程技术领域。在其受压变形过程中，纤维的细观屈曲与结构的宏观失稳紧密相关、互为因果，故长纤维复合材料结构的宏细观失稳现象是典型的多尺度力学行为。寻求其高效准确的建模与仿真方法，确定其关键影响因素，阐明其宏细观失稳相互作用关系，对预测和预防该类现象有重要的科学意义。本项目拟在计算均匀化理论的框架下采用傅里叶级数构造网格尺寸独立于失稳波长的包络线代表体元，以开发宏细观信息双向实时传递的高效均匀化模型。继而，拟采用桥域多尺度方法耦合局部精细模型与所构建的均匀化模型。其中，前者应用在裂纹、纽结等应力集中区域以捕捉局部效应，而后者则用在结构剩余区域以提高计算效率。以此构建的协同多尺度模型兼顾了计算效率与精度，可快速准确地模拟宏细观失稳交互作用下结构的复杂力学响应。最后，拟采用数值渐近法求解多尺度非线性系统，并引入分岔指数以精确预测并跟踪失稳及失效的发生与演化。

长纤维复合材料与结构在压应力作用下的失稳是典型的多尺度力学行为。寻求其高效准确的多尺度建模与仿真方法，探知其关键影响因素及相互作用关系，对预测和预防该类现象有重要的科学意义。为此，本项目一方面在经典计算力学的框架下发展一系列稳健高效的模型缩减技术（傅立叶包络线模型、降维缩减模型等）以及精准的多尺度计算方案（计算均匀化理论、桥域多尺度方法等）；一方面在数据驱动计算力学的框架下提出了一个从本构数据采集到材料结构一体化计算的多尺度计算框架，其核心是高质量数据库构建方法（高保真代表体元几何重建方法、结构基因采集方法等）和高效驱动算法（结构基因驱动算法、树形搜索技术等）。研究结果显示，本项目构建的一系列多尺度计算方案为揭示长纤维复合材料细观属性以及宏观结构响应之间的内在规律提供了可靠的理论基础与技术支持，此外，计算均匀化理论、模型缩减技术、数据采集方案以及数据驱动算法的融合对于拓展力学和数据科学的交叉前沿具有深远的科学意义。依托本项目，项目组在JMPS、CMAME、IJSS、IJES等本领域重要学术期刊上发表SCI论文24篇，获批软件著作权1项，举办国际学术会议2次。研究生参加国际学术会议20余人次，黄威获第二十三届国际复合材料与结构会议“Ian Marshall 最佳学生论文奖”（首位获奖华人）及“武汉大学学术创新奖一等奖”，徐锐获“研究生国家奖学金”，匡增涛获“武汉大学学术创新奖二等奖”。