CDS&E: Data-driven Discovery of Multiscale Failure Dynamics of Brittle Materials with Random Microstructure

This Computational and Data-Enabled Science and Engineering (CDS&E) project will promote the progress of science and advance national prosperity, welfare, and security by creating faster and more trustworthy computational tools for predicting how engineering materials fail. Brittle materials used in aerospace, advanced manufacturing, infrastructure, and defense-relevant systems can fail catastrophically when microstructural defects, pores, inclusions, or cracks interact, localize damage, and propagate under loading. These flaws are often randomly distributed, and their effects evolve across many length and time scales. Detailed simulations can track these processes, but they are too expensive for routine design, uncertainty assessment, and rare failure prediction. Simplified models can reduce this cost, but they often rely on assumptions of regular structure or clear separation of scales that do not hold in real disordered materials. This project will use data-enabled learning and machine learning to discover efficient, interpretable models of how large-scale failure evolves from small-scale randomness. The resulting tools can support safer material design, reduce material waste, and improve confidence in high-consequence failure predictions. The project will train students across multiple educational levels and share open-source software, datasets, tutorials, and course materials. Current approaches for stochastic multiscale failure either resolve fine-scale material variability at high computational cost or impose coarse-scale equations that may not remain valid when localization, disorder, and evolving damage dominate. This project will create a coarse-graining framework that learns coarse-scale evolution equations as local operators from time-dependent fine-scale simulations, rather than assuming variables, averaging rules, or operator form in advance. These operators will advance coarse variables in time over spatial patches without relying on periodic microstructures or scale separation. Neural-network representations and adjoint training methods will learn state-dependent operators efficiently. A symbolic model discovery component will convert the learned dynamics into compact, human-readable equations to improve transparency and transferability. A stochastic modeling component will learn and sample non-stationary and non-Gaussian random fields that represent realistic spatial variability in material properties and defects. The methods will first be verified on benchmark systems with known coarse-scale equations and then applied to brittle fracture problems with random initial damage, strength, and stiffness. The expected contribution is a foundation for interpretable and efficient multiscale modeling under uncertainty, enabling faster uncertainty quantification, rare-event analysis, and reduced models of evolving material failure. The framework may also benefit stochastic multiscale problems in chemistry, biology, and transportation where fine-scale dynamics are known but coarse-scale laws are not. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.