Computational analyses and optimization of thin-walled lattice structures and the application of physics-informed neural networks in computational mechanics

He, Junyan

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https://hdl.handle.net/2142/120498 Copy

Description

Title

Computational analyses and optimization of thin-walled lattice structures and the application of physics-informed neural networks in computational mechanics

Author(s)

He, Junyan

Issue Date

2023-03-17

Director of Research (if dissertation) or Advisor (if thesis)

Jasiuk, Iwona

Doctoral Committee Chair(s)

Jasiuk, Iwona

Committee Member(s)

• Koric, Seid
• Matlack, Kathryn
• Chew, Huck Beng

Department of Study

Mechanical Sci & Engineering

Discipline

Mechanical Engineering

Degree Granting Institution

University of Illinois at Urbana-Champaign

Degree Name

Ph.D.

Degree Level

Dissertation

Keyword(s)

• Thin-walled lattice
• Topology optimization
• Size-dependent properties
• Physics-informed neural networks
• Deep energy method

Abstract

Lattices derive their strength from their structures and can offer specific mechanical properties that are unachievable by the base materials. Previous researchers have employed engineering intuition, bio-inspiration, and topology optimization to design lattice structures for specific purposes. Lattice structures see wide applications as filling materials in sandwich panels, sacrificial cladding layers, and energy absorbers. In their typical application scenarios, it is common for the lattice structures to sustain dynamic loading at high strain rates, such as impact, perforation, and blast waves. The performance of lattice structures can be measured by their specific energy absorption, peak crushing force, mean crushing force, crushing force efficiency, and many other metrics. Finite element simulations are often used to simulate the response of lattice structures. Shell elements are typically used for thin-walled lattices due to their small thickness compared to their other dimensions to improve computational efficiency. This study presents a data-driven approach to studying the structure-property relations for thin-walled lattices with a constant in-plane cross-section. A combinatorial framework is developed to generate lattice cross-section designs randomly. Explicit dynamic finite element simulations are performed to determine the mechanical response under dynamic compression. A deep recurrent neural network model is built to learn the simulated response for different lattice designs and to approximate the structure-property relations within the lattice design space. The results show that a neural network is effective in learning the complex response and, once trained, provides an efficient way to perform preliminary screening of new lattice designs. Besides a data-driven approach, improving the specific energy absorption of thin-walled lattices through topology optimization is also explored in this study. Traditional topology optimization algorithms use solid continuum elements and assume static loads in small deformation with simple material models, which are unsuitable for modeling lattices under large, dynamic deformations. A heuristic optimization framework is proposed and developed, which casts the optimization process as successive updates of lattice walls' thicknesses. Two thickness update schemes are proposed based on the homogenization of field variables (energy density or sensitivity) across all lattice walls. Both are shown to be effective in increasing lattice performance despite the complex dynamic loading and material models involved. Additionally, the effects of lattice wall thickness on mechanical properties are studied. Flat dog-bone tensile specimens with different thicknesses are designed and manufactured via selective laser melting. Quasi-static tests are performed with digital image correlation to measure Young's modulus, yield stress, and elongation to failure. The dependence of these properties on the thickness is obtained via curve fitting and is compiled into a size-dependent material model for numerical simulations. The experimental measurements show that critical mechanical properties decrease with specimen size, and thus it is crucial to account for size effects in numerical simulations of thin-walled lattices. The second part of this study focuses on physics-informed neural networks and their applications in computational solid mechanics. Physics-informed neural networks are an alternative to classical numerical methods like finite elements to find the solution to partial differential equations from scratch. Once trained, they can efficiently infer solutions to similar problems with different loading and boundary conditions. Researchers have developed methods based on the strong form of the governing equation. However, the need to calculate second-order spatial derivatives makes it computationally expensive and can be unstable. This study focuses instead on an alternative method based on an energy formulation known as the deep energy method to broaden its applications. This study develops a topology optimization framework based on the deep energy and adjoint methods. The deep energy method solves the elasticity problem, and the adjoint sensitivity is expressed in terms of the displacement solution. Density-based topology optimization is performed with sensitivity. The results show that iteration time decreases due to transfer learning, and the method can be extended to nonlinear material models. Besides applications in topology optimization, the effects of neural network type and gradient calculation method on solution accuracy are studied. Previous implementations of the deep energy method are limited to a neural network architecture called multi-layer perceptron, and different model architectures need to be sufficiently explored. Therefore, this work explores the use of graph convolutional networks and compares the efficiency and accuracy of the two models. Instead of automatic differentiation, a gradient computation method using finite element shape functions is proposed to avoid numerical instability in coarse meshes. The results show that a graph convolutional network is more accurate than a multi-layer perceptron model, and the new gradient calculation method significantly improves algorithm stability. Finally, this study explores the application of the deep energy method to plasticity. Due to the use of the principle of minimum potential energy in elasticity, deep energy method models have only been applied to elastic deformation. This study attempts to expand the scope of its application to plasticity with the help of a discrete variational formulation of plasticity. The developed method can accurately capture plastic deformation in monotonic and cyclic loadings under isotropic and kinematic hardening models and can efficiently infer the solution fields onto much finer meshes once trained on a coarser mesh.

Graduation Semester

2023-05

Type of Resource

Thesis

Copyright and License Information

Copyright 2023 Junyan He

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