A Multiscale Computational Framework for Ceramic Composite Structures
with Localized Material Nonlinearity
Advisor: Professor Armando Duarte
Abstract
Composite materials are gaining ground as the material of choice in many structural applica5ons. These
tailored materials allow engineers to meet more aggressive design goals, but they bring significant
analysis challenges. Nonlinear material behavior greatly complicates homogeniza5on methods and
mul5scale analysis techniques. In applica5ons like high-speed aircraC, material nonlinearity is an
expecta5on. The loading and environment are too extreme for materials to maintain linear behavior. This
nonlinearity is, however, oCen localized to stress concentra5ons around features like connec5ons, sharp
gradient loads, or areas of high temperature. This disserta5on develops a computa5onal framework that
allows the majority of an analysis domain to use linear elas5c homogenized material proper5es and
coarse, dimensionally-reduced structural models. In localized areas around stress concentra5ons,
material heterogeneity and nonlinearity can be introduced through high-fidelity models capable of
capturing failure. These local areas can appear anywhere in the analysis domain, as needed.
Communica5on across scales allows global behavior to influence local behavior and vice-versa.
A Generalized Finite Element Method with global-local enrichment func5ons (GFEMgl) is the backbone of
this method. Coarse, defeatured global models use linear elas5c, homogenized material models.
Auxiliary local problems capture heterogeneous, nonlinear material behavior and introduce local
structural features, like fasteners. State-of-the-art material models are used to capture damage in
ceramic matrix composites (CMCs) around local structural features. These material models are
introduced via local problems and carried into the global analysis. Modifica5ons to the GFEMgl allow
local problems to be introduced anywhere in the analysis domain. The GFEMgl developed in this work
bridges three material length scales: global homogenized behavior, explicit laminate modeling, and
intraply CMC-specific damage via material models.
The GFEMgl framework is also included in an Itera5ve Global-Local method to create an IGL-GFEMgl
solu5on procedure. Shell elements are the de facto choice for modeling aircraC at the global scale, but
they do not have the resolu5on to capture CMC failure. The IGL-GFEMgl allows global shell models to be
coupled with the proposed GFEMgl framework to capture failure of the CMC material. This creates a
complete analysis loop from a global aircraC model down to the material level, where all scales provide
insight and feedback to one another. This work presents a systema5c study of the proposed mul5scale
analysis method. Relevant CMC material models are developed, calibrated, and validated on their own.
Then the proposed GFEMgl is presented and verified. CMC behavior around open holes and fasteners is
explored with the GFEMgl, including the use of contact models across scales. The method is consistently
compared against industry-adopted mul5scale methods and experiments. The IGL-GFEMgl is then used
to couple global shell models, solved in a commercial soCware, with the GFEMgl framework to capture
local CMC behavior. The computa5onal framework is simple, efficient, and very capable when compared
to compe5ng methods.
