IGFEM-based reduced-order modeling and design of nonlinear composites

Brandyberry, David

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https://hdl.handle.net/2142/109478 Copy

Description

Title

IGFEM-based reduced-order modeling and design of nonlinear composites

Author(s)

Brandyberry, David

Issue Date

2020-10-13

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

Geubelle, Philippe H

Doctoral Committee Chair(s)

Geubelle, Philippe H

Committee Member(s)

• James, Kai
• Tortorelli, Daniel
• Zhang, Xiang

Department of Study

Aerospace Engineering

Discipline

Aerospace Engineering

Degree Granting Institution

University of Illinois at Urbana-Champaign

Degree Name

Ph.D.

Degree Level

Dissertation

Keyword(s)

• Reduced-order model
• optimization
• generalized finite element

Abstract

Motivated by significant advances in manufacturing, development of powerful computational techniques, and increases in computational capacity, the design of material microstructures with specific macroscopic behaviors has been investigated over the past two decades. The main challenges with the solution of these inverse problems is the computational cost associated with modeling the mechanical behavior of complex domains as optimization algorithms are usually iterative, requiring many evaluations of the domain response. For this reason, the majority of existing work on this subject focuses on linear theory. In this work, a powerful nonlinear solver to model the failure of composite materials is developed using an Interface-enriched Generalized Finite Element Method (IGFEM). Cohesive interfacial failure and damage mechanisms in the constituents are the primary source of nonlinearity and the shape of material interfaces and nonlinear damage parameters are the key design variables used to obtain desired nonlinear macroscopic behaviors. Several three-dimensional particulate composite periodic unit cells are optimized to demonstrate the flexibility of IGFEM in the shape optimization process due to its use of a non-conforming mesh. A reduced-order model based on integrating the IGFEM with the Eigendeformation-based reduced-order Homogenization Method (EHM) is then formulated to relieve the extreme computational cost of these large three-dimensional nonlinear finite element evaluations. A multi-resolution optimization scheme is presented to produce microstructure designs near the optimum quickly with the IGFEM-based EHM that are later refined with a high fidelity IGFEM-based optimizer. The damage parameters of several three-dimensional particulate composite microstructures are then designed using this method, showing dramatic deceases in the computational cost and improvements in the final designed material.

Graduation Semester

2020-12

Type of Resource

Thesis

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http://hdl.handle.net/2142/109478

Copyright and License Information

Copyright 2020 David Robert Brandyberry

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