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Multiscale structural optimization through second-order homogenization and machine learning
Dissertation

Multiscale structural optimization through second-order homogenization and machine learning

Nolan Black
Doctor of Philosophy (Ph.D.), Drexel University
Dec 2024
DOI:
https://doi.org/10.17918/00010779
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Black_Nolan_2024100.99 MB
PDF Embargoed Access, Embargo ends: 28 Feb 2027

Abstract

Design optimization Multiscale design Second-order homogenization Computational Mechanics Machine Learning
Multiscale structural design considers the simultaneous configuration of structural features across multiple length scales. Inspired by the design of cellular composites, biological materials, and the rise of additive manufacturing, multiscale design optimization aims to develop the physical models and design methodologies to produce optimized structures with material hierarchy. The computational implementation of multiscale design optimization, however, faces several challenges. The multiscale model must incorporate a demanding, nonlinear relationship at the intersection of fine scale local effects and the greater structural response. Meanwhile, the multiscale design model must define appropriate design features that produce desirable microscale and macroscale behavior. Homogenization-based multiscale finite element analysis has addressed many of these challenges through the resolution of effective microstructural behavior, but homogenization approaches are ultimately limited by prohibitively costly nested analyses. Furthermore, homogenization models rely on an assumption of scale separation such that the microscale physical effects are sufficiently small relative to their macroscale counterpart. This dissertation addresses key challenges in homogenization-based multiscale design by developing machine learning surrogate models that enable efficient modeling and design of multiscale structures. Several approaches to data generation and physics-informed training of neural network surrogates are presented. Equipped with effective machine learning surrogates, a design optimization framework incorporating second-order microstructural behavior is developed to enrich the information exchange in a multiscale design paradigm. This work targets the practical limitations of homogenization-based design while maintaining a strong physical foundation through physics-informed machine learning. The methodologies developed herein enable the study of design optimization techniques subjected to localized stress constraints, length scale and size effects, and multiscale nonlinearities.

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