Topology optimization of multimaterial and multiscale structures beyond elasticity: brittle fracture and ductile plasticity

This dissertation develops a general topology optimization framework for designing multimaterial and multiscale structures subjected to elasticity, plasticity, and fracture under both small and large deformations. The framework embraces both rigorous physics-based methods and general machine learning approaches to predict design performance, which is iteratively improved through gradient-based optimization. The dissertation comprises five interconnected components. It begins with the optimization of multiscale elastic systems, where structures are composed of prescribed building blocks conforming to specific frequency combinations. The framework employs data-driven approaches and deep neural networks to predict the complex frequency–property relationships of the microstructures. The resulting designs enable precise control over local mechanical stress, displacement, and strain energy density, as well as global stiffness. The second component focuses on brittle fracture optimization. A comprehensive phase-field fracture theory is incorporated to capture both fracture nucleation and propagation under small and large deformations. To use this fracture theory, the framework employs physics-consistent interpolation rules for fracture-related properties. Through iterative optimization, the created designs simultaneously maximize initial stiffness, delay crack initiation, and enhance toughness, which lead to the discovery of multiple toughening mechanisms. The third part addresses multimaterial plasticity. The framework employs a rigorous J₂-flow plasticity theory to predict yielding under small and large deformations. A comprehensive sensitivity analysis is developed to handle path-dependence using a reverse adjoint method combined with automatic differentiation. These developments enable the design of diverse multi-alloy systems, including energy-dissipating dampers, load-bearing beams, impact-resistant bumpers, and cold-worked profiled sheets. The fourth component extends plasticity optimization to the multiscale regime, where structures consist of elastoplastic matrix–inclusion microstructures or alloy powder mixtures. To predict their path-dependent and partially unknown constitutive behaviors, a recurrent neural network is embedded into the finite element analysis and topology optimization framework. This integration enables the design of complex elastoplastic and thermoelastoplastic systems such as aircraft blisks. Finally, the dissertation introduces FEniTop — a general FEniCSx-based topology optimization software — capable of solving all the aforementioned design problems. The software flexibly incorporates various physical models through weak-form inputs, while all chain-rule operations are handled via automatic differentiation. It also supports parallel computing for rapid finite element and sensitivity analyses and streamlines the entire process from design to fabrication. Collectively, these five components establish an advanced topology optimization framework capable of addressing multiobjective, multimaterial, and multiscale design tasks involving nonlinearity, coupled-field physics, path dependence, and emerging artificial intelligence. The created optimized designs span applications in civil, mechanical, aerospace, and biomedical engineering. Therefore, this design framework holds great promise for creating the next generation of high-performance materials and structures.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Civil Engineering

Grantor

University of Illinois Urbana-Champaign

Year dc:date

2025

Author dc:creator

• Jia, Yingqi

Contributors dc:contributor

• Zhang, Xiaojia Shelly
• Lopez-Pamies, Oscar
• Duarte, Carlos Armando
• Ning, Xin

• Topology Optimization
• Brittle Fracture
• Plasticity
• Multimaterial
• Multiscale
• Metamaterial
• Neural Networks
• Large Deformations
• Path Dependence
• Nonlinearity

Statement dc:rights

• Copyright 2025 Yingqi Jia

Language dc:language

en

Handle dc:identifier

https://hdl.handle.net/2142/132779

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/132779