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Rudy Geelan "Towards Simple and Predictive Reduced-order Models for Structural Failure"

10:00 am
Friday, February 23, 2024
270 NCB Hall
Faculty Host:  Dr. Rakesh Kapania

Abstract:  The predictive modeling of fracture and failure remains as one of the most significant challenges in the structural mechanics community. While in recent years a variety of methods have received increasing attention, the search for a generally applicable approach remains ongoing. By leveraging the best ideas from various fields of we gain a unique perspective into the challenges that remain. 

One important area of improvement pertains to the simulation-based modeling of failure processes. Variational fracture models promise a unified and mathematically rigorous treatment of fracture evolution in solids. These approaches most commonly find their origin in Griffith's classical theory of brittle fracture. However, there usually exists a process zone in the vicinity of the crack tip which is characterized by small-scale yielding, micro-crack initiation, growth and coalescence. In those cases in which the fracture process zone is sufficiently large compared to the representative size of the structure, cohesive forces in the fracture process zone must be taken into account. This talk will discuss a phase-field formulation of fracture that approximates a cohesive type of response. In contrast to regularized formulations based on Griffith theory of fracture, the effective macroscopic fracture parameters can be held fixed as the regularization length scale is decreased. 

We then turn to model reduction techniques to avoid the need for evaluating fracture simulation models many times with different model parameters and inputs. A reduced-order model provides accurate approximations with orders of magnitude reduction in computational complexity. We consider here projection-based model reduction for computer-based models in which the governing equations of the system of interest are known in advance. A nonlinear model reduction method is proposed that produces parsimonious and interpretable reduced-order models that can be characterized from limited data, as opposed to black-box methods (such as neural networks), which often require an abundance of data yet provide limited physical insight. This is achieved by adopting nonlinear state approximations of polynomial form, a methodology with parallels to manifold learning techniques. By using data-driven operator inference we can then learn reduced-order models directly from available snapshot data.

Bio:  Rudy Geelen is a postdoctoral researcher working with Karen Willcox at the Oden Institute for Computational Engineering and Sciences. He joined UT Austin as a Peter O'Donnell Postdoctoral Fellow in 2020. Before joining UT Austin, he received a Ph.D. in Mechanical Engineering from Duke University. He holds B.S. and M.S. degrees in Mechanical Engineering from the Eindhoven University of Technology in the Netherlands. He is interested in the broad area of computational science and engineering with a strong focus on computational mechanics, model order reduction and scientific machine learning.