When: Feb 16 2022 @ 3:00 PM
Where: Malone G33/35

Zoom Link: https://wse.zoom.us/j/95725896886
In-person Seminar Held in Malone G33/35 (open to first 50 people)

“Towards Trustworthy Geometric Deep Learning for Elastoplasticity”

Presented by Dr. Nikolaos N. Vlassis
Department of Civil Engineering and Engineering Mechanics, Columbia University

Mechanisms at the microstructure scale, such as dislocation, grain rearrangement, and twinning, play a significant role in the macroscopic path-dependent responses of materials. For materials assembled from smaller grains or units, such as polycrystals, granular materials, and architected meta-materials, understanding the evolution of topological and geometrical changes that occur at smaller scales is crucial for improving the accuracy, robustness, and precision of the constitutive response predictions at the macroscale. Conventional material models often rely on handcrafting equations and interpreting discovered causality relations among descriptors, such as porosity, fabric tensor, void distribution, dislocation density. However, this approach is not necessarily optimal for new materials where the key physics are either not fully understood or require the discovery of new descriptors to fully interpret the mechanisms from high-dimensional data (e.g., CT imaging, digital image correlation). This work introduces a meta-modeling framework based on trustworthy artificial intelligence to model the elastoplastic behavior of solids across scales where microstructures are described as graphs. Deep geometric learning algorithms are used to infer low-dimensional descriptors from these weighted graphs to capture the essence of the microstructure’s evolution and how it reflects in the macroscopic response. We decompose the elastoplastic behavior into its theoretically interpretable components – a hyperelastic energy functional and a yield function neural network. The training of the latter is recast as a level set theory problem to enable the geometrical interpretability of the neural network predictions. Methods to ensure the model-based and post hoc interpretability of these neural networks informed by desired mechanical properties (e.g., adherence to thermodynamics, material frame indifference, material symmetry) are also introduced. Potential applications of the proposed framework for experimental design and comparisons with other deep learning models will be provided.

Nick N. Vlassis received his bachelor’s degree in civil engineering and a master’s degree in structural design and analysis of structures from the National Technical University of Athens, Greece in 2017. He received his PhD degree from Columbia University in 2021 and was selected to receive the Mindlin Scholarship for his research on machine learning and data-driven methods for solid mechanics. Since 2021, Nick has been appointed as a postdoctoral research scientist at Columbia University. His current work is funded by the DOE NNSA center and the Air Force Office of Scientific Research.