This Faculty Early Career Development (CAREER) grant will support fundamental research focusing on the integration of complex geometries in predictive stochastic computational modeling. Recent technological breakthroughs in, e.g., additive manufacturing and tissue engineering, have revolutionized the way materials and structures are processed, fabricated, and manufactured. By enabling the production of parts with unprecedented levels of material and geometric complexities over multiple length scales, these breakthroughs have also greatly enhanced the challenges in computational modeling and experimental testing. One of them is the quantification of part response uncertainties over complex geometries. This CAREER project aims to develop a stochastic modeling framework that will enable the automatic and robust integration of complex geometrical features into high-dimensional, predictive computational settings. This approach will pave the way for theoretical developments and virtual testing paradigms in fields where uncertainty in behavior must be quantified on real-world geometries. As part of the project, an extensive educational and outreach plan is also planned. This component notably includes: (1) hands-on research opportunities for undergraduate and graduate students, (2) activities to engage and educate a broad audience on basic science concepts with impactful applications, and (3) activities to increase the participation of K-12 students and underrepresented groups in computational mechanics, materials science, and STEM at large.
This research seeks to bridge the gap between geometrical complexity and uncertainty quantification methodologies. While there has been considerable progress in the development of probabilistic frameworks accounting for multiple sources of uncertainties in computational physics, the proper integration of complex (e.g., nonconvex) geometrical descriptions into stochastic approaches remains mostly unexplored. In this case, the characteristics of the geometrical features and the intrinsic properties of material uncertainties are intertwined through processing conditions, which uniquely challenges the state-of-the-art in stochastic modeling and uncertainty quantification. To advance new knowledge and tools, the objectives of this project include: (1) the development of appropriate probabilistic representations for a broad class of stochastic constitutive models across (spatial) scales, (2) the construction of efficient generators for sampling on complex large-scale domains, and (3) the development of robust probabilistic methodologies for model identification, propagation, and validation. To address these issues, the research will combine theoretical derivations for stochastic modeling on constrained state spaces, computational developments for random generation through fractional partial differential equations, Bayesian inference for underdetermined statistical inverse problems, and experimental characterization on additively-manufactured bone-like titanium scaffolds.
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.
