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

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.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Aerospace Engineering

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2021

Author dc:creator

• Brandyberry, David

Contributors dc:contributor

• Geubelle, Philippe H
• James, Kai
• Tortorelli, Daniel
• Zhang, Xiang

• Reduced-order model
• optimization
• generalized finite element

Statement dc:rights

• Copyright 2020 David Robert Brandyberry

Language dc:language

en

Handle dc:identifier

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

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/109478