GUO-DISSERTATION-2017

180 Pages·2017·7.78 MB·English

A Coupled Multi-physics Analysis Model for Integrating
Transient Electro-Magnetics and Structural Dynamic Fields
with Damage
by
Shu Guo
A dissertation submitted to The Johns Hopkins University in conformity with the
requirements for the degree of Doctor of Philosophy.
Baltimore, Maryland
May, 2017
(cid:13)c Shu Guo 2017
All rights reserved
Abstract
The development of advanced material processing and the appearance of novel
materials introduce a broad and promising area of multi-functional structures. The
improvements of these structures over the traditional ones are the various capabilities
to perform multiple tasks. Multi-physics phenomena, such as mechanical (ME) and
electromagnetic (EM) coupling, are fundamental to study such structures. Some ex-
amples of these structures may be components of small unmanned airborne vehicles
(UAVs), active skins of aircraft, or meta-materials for optical and communication
systems. There is a need for a robust, coupled multi-physics computational model
and codes supporting meaningful design of multi-functional structures and devices.
In this dissertation, a generalized framework is developed for coupling EM and
dynamic ME fields under finite deformation. To achieve a versatile and robust cou-
pling scheme between fields, the problems are solved in a staggered way using a
time-domain finite element (FE) method by a high performance parallel program.
The deformation information from solved ME field is used to obtain the EM field in
the same configuration. To account for finite deformation and its effects on the EM
fields, a Lagrangiandescription is invoked for both ME field and EM field. Unlike tra-
ii
ditional scheme to simulate EM field, the coupling scheme maps Maxwell’s equations
from spatial to material coordinates in the reference configuration. For a efficient
solution, a scalar potential and vector potentials are chosen as independent solution
variablesinlieuofEMfieldvariablestoreducethedegreeoffreedom. Non-uniqueness
in the solution of the reduced set of equations is overcome through the introduction
of a gauge condition in the FE formulations. The boundary conditions are appro-
priatelyrepresented intermsofthepotentialsthatdonotrepresent physicalvariables.
A high performance, parallel code in FE method is developed to solve the multi-
physics problems. The computational domain is decomposed and distributed to mul-
tiple processors using the ParMETIS library. Subsequently, the Portable, Extensible
Toolkit for Scientific Computation or PETSc library, which is a Message Passing In-
terface (MPI) based library, is employed to accomplish the parallelization of the code
for assembling and solving both the ME and the EM problems. Selected features of
the code are validated using existing solutions in the literature, as well as comparison
with results of simulations with commercial software. Convergence and accuracy of
the code are examined.
In view of functionality of different devices, two sets of multi-physics phenomena
are studied thoroughly using the framework. The load-bearing antenna application
requires the coupling between transient EM and dynamic ME fields. The simulations
iii
predict the evolution of electrical and magnetic fields and their fluxes in a vibrating
substrate undergoing finite deformation. In this application, the Lorentz force gener-
ated in the coupling is negligible compared with the external applied mechanical load.
Thus, the coupling is only one-way from the ME field to the EM fields. The effects of
mechanical load frequency, amplitudes and direction on EM fields are investigated.
Furthermore, a novel self-sensing piezoelectric sensor is introduced by implement-
ing a three-dimensional isotropic damage model with piezoelectric material. In the
contrasttotheload-bearingantennaapplication,two-waycouplingofelectricfieldand
ME field is necessary through piezoelectricity. The piezoelectric coupling is achieved
in the reference configuration to accommodate the coupling under finite deforma-
tion. The damage criterion is established from the maximum deviatoric strain energy
throughout the mechanical loading history. The degradation impacts on both me-
chanical stiffness and piezoelectric coupling constant. The damage developed in the
structure can be predicted by the electric field generated from piezoelectricity. The
difference of the electric field between damaged and undamaged structure is employed
to correlate with the damage parameter and its time derivative. A rigorous functional
form is proposed for the correlation function. The model is calibrated and validated
by different simulation cases.
iv
Dissertation Committee:
Professor Somnath Ghosh, Advisor
Professor Benjamin W. Schafer
Professor James K. Guest
Professor Sung Hoon Kang
Professor Michael D. Shields
v
Acknowledgments
As I compose the dissertation to summarize my PhD work, all the days in the
journey to pursue the degree come back, vividly. I remembered the early days when
I was struggling with basic knowledge of electromagnetics as a fresh PhD with no
experience in it. I cannot forget the sleepless nights when I was working hard for the
results and slides for the reviews. All the endeavor in days and nights pays off to the
contents inthisdissertation. Inthisprocess, myadvisor, Prof. SomnathGhosh, guide
me as a patient teacher, a rigorous scientist and a kind father. I admire his spirit to
pursue perfection, his vision to build up research and I am consistently inspired to
become a phenomenal researcher like him one day.
I am very grateful to Prof. Benjamin W. Schafer, Prof. James K. Guest, Prof.
Sung Hoon Kang and Prof. Michael Shields for being on my committee. My deepest
thanks to my friends and lab-mates in Computational Mechanics Research Lab for
their constant help in research, moral support and companionship.
I would like to express my sincere gratitude to Qi Wu, my beloved wife, for her
endless support and caring. My sincerest love and gratitude to my parents and
parents-in-law and my families for their patience and love.
My sincere thanks to Dr. B. L. (”Les”) Lee from Mechanics of Multifunctional
vi
Materials & Microsystems division of AFOSR for the financial support of the work.
The work is done under subcontract to Johns Hopkins University under award ID
2770925044895D. The sponsorship is greatly appreciated. I want to thank the staffs
at Ohio Supercomputer Center, Homewood High-Performance Cluster and Maryland
AdvancedResearchComputingCenter forhelpingmeworkwiththesuper-computers.
vii
To Qi and upcoming Chelsea, the warmest stars guide me home, always.
viii
Contents
Abstract ii
Acknowledgments vi
List of Tables xiv
List of Figures xv
1 Introduction 1
1.1 Organization of the Thesis . . . . . . . . . . . . . . . . . . . . . . . . 8
2 Finite Element Model for Coupled Transient Electromagnetic and
Dynamical Mechanical Field 10
2.1 Governing Equations for the Finite Deformation Dynamics Problem . 12
2.1.1 Some Hyperelastic Material Models . . . . . . . . . . . . . . . 12
2.1.1.1 Neo-Hookean Material Model . . . . . . . . . . . . . 12
2.1.1.2 Modified Neo-Hookean Material Model . . . . . . . . 14
2.1.1.3 Logarithmic Stretch Model . . . . . . . . . . . . . . 16
2.1.2 Strong Form for the Finite Deformation Dynamics Problem . 17
2.2 Governing Equations for the Electromagnetic Problem in Current and
Reference Configurations . . . . . . . . . . . . . . . . . . . . . . . . . 21
ix
2.2.1 Scalar and Vector Potentials in Current and Reference Config-
urations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
2.2.2 Constraint Gauge Condition for Solution Uniqueness . . . . . 32
2.3 Weak Forms of Coupled ME-EM Problem . . . . . . . . . . . . . . . 33
2.3.1 Weak Form and Boundary Conditions of the Finite Deforma-
tion Dynamics Problem . . . . . . . . . . . . . . . . . . . . . 34
2.3.2 Weak Form of the Electromagnetic Problem in the Reference
Configuration . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
2.3.2.1 Boundary Conditions in Terms of the Potentials . . . 41
2.4 Finite Element Implementation of Coupled ME-EM Problem . . . . . 44
2.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
3 Piezoelectric ConstitutiveEquations withContinuum Damage Model
in the Reference Configuration 53
3.1 Piezoelectric Material Model in Coupled Electric Field with Finite De-
formation Setting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
3.1.1 Piezoelectric Material Constitutive Equations in the Current
Configuration . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
3.1.2 Piezoelectric Material Constitutive Equations in the Reference
Configuration . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
3.1.3 Objectivity of the Piezoelectric Material Constitutive Equa-
tions in the Reference Configuration . . . . . . . . . . . . . . 62
x