Concurrent Stochastic Characterization of Mesoscale Material Heterogeneities and Macroscale Structural Complexities

由于缺失或未建模的特征及其在多个长度尺度上的相互作用，使用计算机模型对结构行为进行可靠预测，特别是对于复杂和柔性的结构系统，通常几乎是不可能的。一方面，复杂的结构系统可以由附接到主结构部件的许多子部件（例如，飞机机翼或整个飞机），跨度达数十米。另一方面，在毫米及以下的更精细尺度下，微缺陷（例如，在金属和合金的晶粒中）可能需要被总结并结合到不同结构部件的材料模型中，这是由于它们对它们的行为的潜在影响。现有的计算算法、硬件容量和存储器要求尚不能精确地复制所描述的复杂结构系统的整体，这可能导致计算预测显著偏离实际行为。本研究探讨了如何通过引入中尺度不确定性和宏观尺度不确定性的概念来理解高度复杂的结构行为，以纳入未建模特征的影响，同时绕过在实践中根本不可行的建模保真度的极端水平。其结果将有助于在许多应用，包括航空航天，机械，民用，岩土工程，海军和生物力学应用中的新的和老化的复杂结构系统的规定改进的设计准则。作为该项目的一部分，PI还将让高中、本科、研究生和代表性不足的学生参与各种研究和教育活动，如在线自我评估测试、期刊俱乐部组织、本研究的目的是设计一个随机矩阵理论（RMT）基于预测框架，可以概率地表征数百微米到数十或数百米尺度的缺失或未建模特征。例如，在介观尺度上的未建模特征指的是材料颗粒的形状、取向和分布的变化，以及在结构材料（例如钢和合金）中微裂纹的存在或不存在，而在系统水平上的未建模特征指的是有缺陷的边界条件、不完美的界面/接头、以及缺乏关于结构子部件的几何和材料特性的准确信息。这里采用基于RMT的概率模型来合并这些特征的效果，而不依赖于常规模型参数的直接随机化（例如，年轻？s模量、弹簧常数等）。项目？的方法提供了一种替代的建模方法，传统的或参数的概率方法，特别是，复杂的系统，涉及许多传统的模型参数。

Reliable prediction of structural behavior, particularly for complex and flexible structural systems, using computer models is often next to impossible due to missing or un-modeled features and their interactions at multiple length scales. On one hand, a complex structural system may consist of numerous subcomponents attached to a primary structural component (e.g., an aircraft wing or the entire aircraft) that spans to tens of meters. On the other hand, at finer scales of millimeters and below, presence and variations of micro-defects (e.g., in the grains of metals and alloys) may need to be summarized and incorporated into the material models of different structural components due to their potential influence on their behavior. Existing computational algorithms, hardware capacity, and memory requirements are not yet capable of precisely replicating the entirety of complex structural system as described, which may cause computational predictions to significantly deviate from the actual behavior. This research investigates how a highly complex structural behavior may be understood by introducing the concepts of mesoscale uncertainty and macroscale uncertainty to incorporate the effects of unmodelled features, while bypassing the extreme level of modeling fidelity which is simply not feasible in practice. The outcome will facilitate in prescribing improved design guidelines for new and aged complex structural systems in many applications including aerospace, mechanical, civil, geotechnical, naval, and biomechanical applications. As part of the project, the PI will also engage high-school, undergraduate, graduate, and underrepresented students in various research and educational activities, such as online self-evaluation testing, journal club organization, and active learning incorporation in undergraduate teaching.The objective of this research project is to devise a random matrix theory (RMT) based predictive framework that can probabilistically characterize missing or unmodelled features at the scale of a few hundreds of micrometers to tens or hundreds of meters. The unmodelled features at the mesoscale refer to, for instance, variations in shapes, orientations, and distribution of material grains, and presence or absence of micro-cracks in structural materials such as steel and alloys, while the unmodelled features at the system level allude to the effects of faulty boundary conditions, imperfect interfaces/joints, and lack of accurate information about geometrical and material properties of structural subcomponents. The RMT based probabilistic models are employed here to incorporate the effects of these features without relying on direct-randomization of the conventional model parameters (e.g., Young?s modulus, spring constants, etc.). The project?s approach provides an alternative modeling approach to the traditional or parametric probabilistic approach, particularly, for complex systems involving many conventional model parameters.