Use of Shape-Memory Alloy Devices in Earthquake Engineering

145 Pages·2005·1.81 MB·English

Universit`a degli Studi di Pavia
ROSE School
EUROPEAN SCHOOL FOR ADVANCED STUDIES IN
REDUCTION OF SEISMIC RISK
Use of Shape-Memory Alloy Devices in Earthquake
Engineering: Mechanical Properties, Advanced
Constitutive Modelling and Structural Applications
A Thesis Submitted in Partial Fulfilment of the Requirements
for the Doctor of Philosophy Degree in
EARTHQUAKE ENGINEERING
by
DAVIDE FUGAZZA
Advisors: Prof. Ferdinando Auricchio (Universit`a degli Studi di Pavia)
Prof. Reginald DesRoches (Georgia Institute of Technology)
Pavia, August 2005
ABSTRACT
Shape-memory alloys (SMAs) are a class of solids showing mechanical properties
not present in materials usually utilized in engineering. SMAs have the ability
to undergo reversible micromechanical phase transition processess by changing
their cristallographic structure. This capacity results in two major features at
the macroscopic level which are the superelasticity and the shape-memory effect.
Dueto theseuniquecharacteristics, SMAmaterials lendthemselves toinnovative
applications in many scientific fields, ranging from biomedical devices, such as
stents or orthodontic archwires, to apparatus for the deployment and control of
space structures, such as antennas and satellites.
Recent experimental and numerical investigations have also shown that the use
of SMAs as vibration control devices seems to be an effective mean of improving
the dynamic response of buildings and bridges subjected to earthquake-induced
excitations.
Inthisrespect,thepresentworkfocusesontheseismicperformanceofsteelframes
equipped with either steel or superelastic SMA braces, in order to evaluate the
possibility of adopting an innovative bracing system in place of a traditional one.
Also, a contribution on the modelling of superelastic SMA materials for seismic
applications is given and two uniaxial rate-dependent constitutive equations are
developed, implemented and compared with experimental data.
Finally, preliminary results concerning shake table tests of a reduce-scale frame
equipped with superelastic SMA braces are provided and numerical results from
the corresponding finite element study are reported and discussed.
Keywords: shape-memory alloys, constitutive modelling, experimental data,
seismic protection devices, steel buildings, bracing systems, dynamic analysis,
earthquake engineering.
ii DavideFugazza
The dissertation is organized in 7 Chapters and 3 Appendices as follows:
Chapter 1 overviews the main features of SMAs. It also explains the reason
for the increasing interest in such new materials through a survey of the most
important applications nowadays exploited.
Chapter 2 investigates the mechanical properties of SMAs by reviewing the
experimental works available in the literature. The structural behavior of SMA
wires, bars and plates is discussed in view of their potential use as innovative
seimic devices.
Chapter 3proposesanupdatedstate-of-the-art reviewontheuseofSMA-based
devices inearthquake engineering. Attention is devoted to numerical, experimen-
tal and existing applications.
Chapter 4 concentrates on the structural applications. An extensive campaign
of numerical simulations is performed on steel buildings equipped with either
traditional steel braces or innovative superelastic SMA braces for the evaluation
of their seismic performance.
Chapter 5 focuses on the constitutive modelling of SMAs for seismic applica-
tions. Two rate-dependent uniaxial constitutive models for superelastic SMAs
are developed and implemented and their ability to simulate experimental data
is assessed.
Chapter 6 shows the preliminary results of an experimental investigation deal-
ing with shake table tests of a reduced-scale frame endowed with superelastic
SMA wires as bracing system. Comparisons with a finite element study are also
provided.
Chapter 7 concludes the dissertation by summarizing the most important find-
ings as well as by proposing some ideas for further research.
UseofShape-MemoryAlloyDevicesinEarthquakeEngineering iii
Appendix A reports the acceleration time-histories of the seismic inputs used
for the numerical simulations as well as a summary of their characteristics.
Appendix B provides the mathematical expressions needed to integrate the
proposed constitutive models via iterative strategy.
Appendix C lists the algebraic coefficients needed to integrate the proposed
constitutive models in closed-form.

ACKNOWLEDGMENTS
I wishto express my most sincere gratitude to my advisors, Professor Ferdinando
Auricchio and Professor Reginald DesRoches. I have had a great and fruitful ex-
perienceworkingwiththem andI really hopethatourcollaboration can continue
in the future.
I am indebted with Professor Auricchio for his continuous help, assistance and
advice during these years and since the first time I met him. I also thank him
for introducing me to the Rose School and to Georgia Tech.
IamverygratefultoProfessorDesRoches forgivingmethepossibility ofworking
with him in the United States. That was a dream come true. I did have a good
time in Atlanta and I really thank him so much for his kindness.
IwouldliketothanktheItalian National SeismicSurveryforprovidingthePh.D.
scholarship as well as the University of Pavia for the research fundings provided
through the PRIN Project ”Shape-memory alloys: constitutive modeling, struc-
tural behavior, experimental validation and design of biomedical devices” and
the Progetto Giovani Ricercatori - Bando 2002. Also, the support offered by
the School of Civil and Environmental Engineering of the Georgia Institute of
Technology is kindly acknowledged.
Finally, a very special thank goes to my family and to my closest friends for their
continuous support and encouragement, specially when I was abroad.
Pavia, August 2005

TABLE OF CONTENTS
Abstract................................................................. i
Acknowledgements....................................................... v
Table of Contents....................................................... vi
List of Tables............................................................ xi
List of Figures........................................................... xiii
1. General Characteristics of Shape-Memory Alloys................... 1
1.1.Introduction........................................................ 1
1.2.General Features and Phase Transformations ........................... 1
1.3.Superelasticity and Shape-Memory Effect .............................. 2
1.4.An Example of Shape-Memory Alloy Material: Nitinol................... 3
1.5.Applications........................................................ 3
2. Mechanical Behaviour of Shape-Memory Alloy Elements............ 9
2.1.Introduction........................................................ 9
2.2.Mechanical Behaviour of SMA Wires, Bars and Plates ................... 9
3. Use of Shape-Memory Alloys in Earthquake Engineering............ 17
3.1.Introduction........................................................ 17
viii DavideFugazza
3.2.Numerical Applications .............................................. 17
3.3.Experimental Applications ........................................... 19
3.4.Existing Applications................................................ 21
4. Seismic Performance of Steel Frames equipped with Traditional and
Innovative Braces..................................................... 29
4.1.Introduction........................................................ 29
4.2.Earthquake Records and Frame Characteristics ......................... 29
4.3.OverviewontheConstitutiveModellingofShape-MemoryAlloysforSeismic
Applications........................................................ 30
4.4.Finite Element Platform and Modelling Assumptions .................... 31
4.5.Design of Superelastic Shape-Memory Alloy Braces...................... 32
4.6.Results and Discussion............................................... 33
4.6.1.Buckling-allowedsteel braces vs. superelastic SMA braces........... 33
4.6.2.Buckling-restrainedsteel braces vs. superelastic SMA braces......... 34
5. Advanced Uniaxial Constitutive Models for Superelastic Shape-
Memory Alloys........................................................ 45
5.1.Introduction........................................................ 45
5.2.Development of a Rate-Dependent Viscous Constitutive Model............ 45
5.2.1.Time-continuous general framework .............................. 45
5.2.2.Kinetic Rules .................................................. 46
5.2.3.Evolution of elastic modulus..................................... 48
UseofShape-MemoryAlloyDevicesinEarthquakeEngineering ix
5.2.4.Stress-strainrelationship ........................................ 48
5.2.5.Time-discrete model............................................ 49
5.2.6.Solution algorithms............................................. 51
5.3.Development of a Rate-Dependent Thermo-Mechanical Constitutive Model. 52
5.3.1.Time-continuous general framework .............................. 52
5.3.2.Kinetic rules................................................... 52
5.3.3.Evolution of elastic modulus..................................... 54
5.3.4.Free energy.................................................... 54
5.3.5.Stress-strainrelationship ........................................ 55
5.3.6.Heat equation ................................................. 55
5.3.7.Time-discrete model............................................ 56
5.3.8.Solution algorithms............................................. 57
5.4.Numerical Simulations............................................... 58
5.4.1.Model response ................................................ 59
5.5.Experimental Investigation and Material Parameter Selection............. 61
5.5.1.Material parameter selection for viscous model..................... 62
5.5.2.Material parameter selection for thermo-mechanicalmodel .......... 62
5.6.Ability of the Models to reproduce Experimental Data................... 63
5.7.Concluding Remarks ................................................ 64