S5E13

Abstract

Metamodels, or models of models, map defined model inputs to defined model outputs. When metamodels are constructed to be computationally cheap, they are an invaluable tool for applications ranging from topology optimization, to uncertainty quantification, to real-time prediction, to multi-scale simulation. In particular, for heterogeneous materials, metamodels are useful for exploring the influence of the (potentially massive) heterogeneous material property parameter space. By nature, a given metamodel will be tailored to a specific dataset. However, the most pragmatic metamodel type and structure will often be general to larger classes of problems. At present, the most pragmatic metamodel selection for dealing with mechanical data — specifically simulations of heterogenous materials — has not been thoroughly explored. In this work, we draw inspiration from the benchmark datasets available to the computer vision research community. These benchmark datasets have both made it feasible to compare different methods for solving the same problem, and inspired new directions for method development. In response, we introduce benchmark datasets for engineering mechanics problems (for example, the Mechanical MNIST Collection https://open.bu.edu/handle/2144/39371 [1,2,3]). Then, we show some example problems that we are exploring with these datasets such as our methodology for constructing metamodels for predicting full field quantities of interest (e.g., full field displacements, stress, strain, or damage variable), and for leveraging information from multiple simulation fidelities, and for predicting out of distribution behavior. Looking forward, we anticipate that disseminating both these benchmark datasets and our computational methods will enable the broader community of researchers to develop improved techniques for understanding the behavior of spatially heterogeneous materials. We also hope to inspire others to use our datasets for educational and research purposes, and to disseminate datasets and metamodels specific to their own areas of interest (https://elejeune11.github.io/).

[1] Lejeune, E. (2020). Mechanical MNIST: A benchmark dataset for mechanical metamodels. Extreme Mechanics Letters, 36, 100659.

[2] Lejeune, E., & Zhao, B. (2020). Exploring the potential of transfer learning for metamodels of heterogeneous material deformation. Journal of the Mechanical Behavior of Biomedical Materials, 104276.

[3] Mohammadzadeh, S., & Lejeune, E. (2022). Predicting mechanically driven full-field quantities of interest with deep learning-based metamodels. Extreme Mechanics Letters, 50, 101566.

Website link: https://sites.bu.edu/lejeunelab/

Introduction of speaker

Emma Lejeune is an Assistant Professor in the Mechanical Engineering Department at Boston University. She received her PhD from Stanford University in September 2018, and was a Peter O’Donnell, Jr. postdoctoral research fellow at the Oden Institute at the University of Texas at Austin until 2020 when she joined the faculty at BU. At BU, Emma has received the David R. Dalton Career Development Professorship, a Computational Science and Engineering Junior Faculty Fellowship, the Haythornthwaite Research Initiation Grant from the ASME Applied Mechanics Division, and the American Heart Association Career Development Award. Current areas of research involve integrating data-driven and physics based computational models, and characterizing and predicting the mechanical behavior of heterogeneous materials and biological systems.

Abstract

Can the mathematical framework developed for constitutive nonlinearities be extended to arbitrary dimensions so as to capture macroscopic effects, such as structural relationships between forces and displacements? In this work, the mathematics developed to capture classical plasticity (i.e., the nonlinear relationships between the six components of stress and strain) are leveraged to describe general nonlinear force-displacement responses. Herein, we develop nonlinear substructures, which provide a method to describe structural relationships between force and displacement associated with various degrees of freedom essential for prediction of global response, these being considered as only analogous to stresses and strains. We draw inspiration from linear substructure analysis, a historical structural model order reduction method, and extend the method to consider general nonlinear responses by leveraging the mathematical framework developed for computational plasticity. While the latter provides nonlinear constitutive relationships between six independent stress and strain components, we show that the same mathematical formulation can capture similar relations between an arbitrary number of forces and displacements (i.e., the retained degrees of freedom). The developed nonlinear substructure method is then demonstrated by analyzing a sweep morphing wing comprised of an array of multi-material unit cells at reduced computational cost but sufficient accuracy.

Introduction of speaker

Patrick is a National Research Council postdoctoral fellow at the Air Force Research Laboratory with joint appointments in the Aerospace Systems Directorate and Materials and Manufacturing Directorate. He received his BS in Mechanical Engineering from Lehigh University, and his MS and Ph.D. from Texas A&M University. His research focuses on reduced-order modeling methods for structural design with an emphasis on physics-based or physics-inspired approaches.