Concurrent Stochastic Characterization of Mesoscale Material Heterogeneities and Macroscale Structural Complexities

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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.