Modeling Complex Behavior of Lattices to Enable Multiscale Design

Project Overview

Micro-architected materials (MAMs) contain complex but controlled fine-scale geometry that includes void space. Such materials are increasingly able to be produced at scale in a variety of base materials, (metals, polymers, and ceramics) as advanced manufacturing methods continue to improve. Previous work has shown that MAMs can be made stiffer and stronger than traditional low-density materials like foams, and they can be functionally graded through a part. Thus, to obtain optimal structures, a designer must not only consider traditional choices like alloy and heat treatment, but now also the spatially-varying details of the fine-scale geometry, which is an extremely high-dimensional space. Our aim in this project was to develop computational tools to enable designers to efficiently create optimal designs across a range of applications.

Our approach was to apply mathematical homogenization and reduced-order modeling techniques to high-fidelity finite element analyses (FEA) that capture the details of the fine-scale geometry, and sample selected, known-manufacturable designs across a range of geometries. These sample points were then used to train differentiable machine learning models, which are then used with traditional gradient-based topology optimization to find optimal structures. We have successfully developed many dozens of such models and can now design for general thermal and mechanical figures of merit, and have additional specialized models for creeping flow and acoustic and electromagnetic meta-materials. Additionally, in producing these models we have developed modular tools and workflows for meshing, simulation, and machine learning that can be applied beyond the MAMs we considered in this project, to consider additional fine-scale geometries, or variation or uncertainty in those geometries, and to additional physics.

Mission Impact

With the completion of this project, we have developed computational models that allow designers to efficiently create and accurately simulate functionally-graded MAMs. Our FEA-based models enhance our fundamental understanding of the response of lattice materials beyond that provided by first-generation models based on simpler simulations. These earlier models are prone to being applied outside their range of validity, and thus the models developed on this project reduce uncertainty in the predicted response of MAMs. Since these models were created specifically for compatibility with gradient-based optimization tools, they also enhance agility in design, as new functionally-graded MAMs can be created rapidly in response to changing design requirements. Finally, the tools used to produce these models are modular and provide capabilities to meet future national security challenges.

Publications, Presentations, and Patents

Dalklint, Anna, Mathias Wallin, and Daniel A. Tortorelli. 2021. "Structural Stability and Artificial Buckling Modes in Topology Optimization." Structural and Multidisciplinary Optimization 64: 1751-1763.

Dalklint, Anna, Mathias Wallin, Katia Bertoldi, and Daniel Tortorelli. 2022. "Tunable Phononic Bandgap Materials Designed via Topology Optimization." Journal of the Mechanics and Physics of Solids 163: 104849.

Ivarsson, Niklas, Mathias Wallin, Oded Amir and Daniel A. Tortorelli. 2021. "Plastic Work Constrained Elastoplastic Topology Optimization." International Journal for Numerical Methods in Engineering. 122:4354-4377.

Swartz, Kenneth E., Daniel A. Tortorelli, Daniel A. White, and Kai A. James. 2022. "Manufacturing and Stiffness Constraints for Topology Optimized Periodic Structures." Structural and Multidisciplinary Optimization. 65(129): 1-20.

Swartz, Kenneth E., Daniel A. White, Daniel A. Tortorelli, and Kai A. James. 2021. "Topology Optimization of 3D Photonic Crystals with Complete Bandgaps." Optics Express. 29(14): 22170-22191.

Wallin, Mathias, Anna Dalklint and Daniel Tortorelli. 2021. "Topology Optimization of Bistable Elastic Structures — An Application to Logic Gates." Computer Methods in Applied Mechanics and Engineering 383: 113912.

Zhang, Z. J., Adrian Butscher, Seth Watts, and Daniel A. Tortorelli. 2022. "Anisotropic yield models for lattice unit cell structures exploiting orthotropic symmetry." Computer Methods in Applied Mechanics and Engineering. 394: 114935.

Wallin, Mathias, Niklas Ivarsson, Oded Amir and Daniel Tortorelli. 2020. "Consistent Boundary Conditions for PDE Filter Regularization in Topology Optimization." Structural and Multidisciplinary Optimization. 62: 1299-1311.

Dalklint, Anna, Mathias Wallin, and Daniel A. Tortorelli. 2021. "Topology optimization of eigenvalue problems." 14th World Congress on Structural and Multidisciplinary Optimization, Boulder, CO, June 2021.

Gillette, Andrew. "Delaunay-Guided Neural Network Design." Colorado State Applied Math Seminar, Virtual. February 2021.

Gillette, Andrew. "Delaunay-Based Assessment of Variational Autoencoders." SIAM Conference on Computational Science and Engineering, Virtual, March 2021.

Gillette, Andrew. "How Can You Know if Nour Neural Network is Doing a Good Job?" LLNL Computing Scholars Seminar Series, Livermore, CA. July 2021.

Gillette, Andrew. "Delaunay Rate Check Diagnostics for Model Assessment." CASC Work-In-Progress Seminar, Livermore, CA. October 2021.

Gillette, Andrew. "Why are Mathematicians Jumping on the Machine Learning Bandwagon?" DOE Computational Research Leadership Council Seminar, California State University, Fresno, CA. November 2021.

Gillette, Andrew. "Delaunay Interpolation Diagnostics for Model Assessment." Center for Mathematics and Artificial Intelligence Colloquium, George Mason University, December 2021.

Gillette, Andrew. "Data-Driven Geometric Scale Detection via Delaunay Interpolation." WPD/WSC Cognitive Simulation and Machine Learning Workshop, Livermore, CA. March 2022.

Gillette, Andrew. "Barycentric Coordinates in General Dimensions." Congressi Stefano Franscini Workshop on Generalized Barycentric Coordinates, Ascona, Switzerland. June 2022.

Granlund, Gunnar, Mathias Wallin, and Daniel A. Tortorelli. "Stress Constrained Topology Optimization." 14th World Congress on Structural and Multidisciplinary Optimization, Boulder, CO. June 2021.

Swartz, Kenneth. "Topology Optimization of Photonic Crystals with Elasticity Constraints." 14th World Congress on Structural and Multidisciplinary Optimization, Boulder, CO. June 2021.

Villanueva, Hernan, Daniel White, Jun Kudo, Charles Jekel, Daniel Tortorelli, and Seth Watts. "Shape Optimization of Cellular Structures Using a Reduced Order Model. 15th World Congress on Computational Mechanics, Yokohama, Japan. August 2022.

Wallin, Mathias, Niklas Ivarsson, Oded Amir, and Daniel A. Tortorelli. 2021. "Plastic work constrained topology optimization." 14th World Congress on Structural and Multidisciplinary Optimization, Boulder, CO. June 2021.

Watts, Seth. "Simple, Accurate Surrogate Models of the Elastic Response of Three-Dimensional Open Truss Micro-Architectures with Applications to Multiscale Topology Design." TOP webinar 7, hosted by Technical University of Delft, Netherlands. November 2020.

Watts, Seth. "Multiscale Topology Optimization of Lattice Structures Using Fast Surrogate Models," LLNL Computational Engineering Division Technical Forum, Livermore, CA. July 2020. LLNL-ABS-840224.