Electromagneto-Mechanics of Material Systems and Structures E-Book

Yasuhide Shindo

• Herausgeber: John Wiley & Sons
• Kategorie: Fachliteratur
• Sprache: Englisch

Seitenzahl: 323

Veröffentlichungsjahr: 2016

Beschreibung

Electromagneto-Mechanics of Material Systems and Structures

Electromagneto-Mechanics of Material Systems and Structures

Written by a leading expert, this book is a comprehensive introduction to the fundamentals and the state of the art in the electromagneto-mechanics of adaptive materials. Its varied topic range includes an overview on how electric, magnetic, and deformation fields interact with each other in the presence of advanced materials systems, such as electric conductors, dielectrics, ferromagnets, among others. Within this context, the author considers for each material system specific phenomena like vibrations, wave propagation, fracture, and fatigue. Readers will also gain a thorough understanding of applications in the electronics and nuclear energy industries, as well as in smart materials and MEMS.

• Covers a wide and varied range of subject areas, spanning theoretical, experimental, computational studies as well as industrial applications
• Features extensive applications in the electronics, nuclear engineering, smart materials and MEMS industries
• Takes the reader from fundamental concepts, applied research, applications through to emerging technologies

Electromagneto-Mechanics of Material Systems and Structures is an all-in-one reference for advanced/graduate students in mechanical and electrical engineering, as well as materials science. It also serves as a handy refresher guide for engineers in related areas such as aeronautical and civil engineering.

Leseprobe

Table of Contents

Cover

Title Page

Copyright

About the Author

Preface

Acknowledgments

Chapter 1: Introduction

References

Chapter 2: Conducting Material Systems and Structures

2.1 Basic Equations of Dynamic Magnetoelasticity

2.2 Magnetoelastic Plate Vibrations and Waves

2.3 Dynamic Magnetoelastic Crack Mechanics

2.4 Cracked Materials Under Electromagnetic Force

2.5 Summary

References

Chapter 3: Dielectric/Ferroelectric Material Systems and Structures

Part 3.1 Dielectrics

3.1 Basic Equations of Electroelasticity

3.2 Static Electroelastic Crack Mechanics

3.3 Electroelastic Vibrations and Waves

3.4 Dynamic Electroelastic Crack Mechanics

3.5 Summary

Part 3.2 Piezoelectricity

3.6 Piezomechanics and Basic Equations

3.7 Bending of Piezoelectric Laminates

3.8 Electromechanical Field Concentrations

3.9 Cryogenic and High-Temperature Electromechanical Responses

3.10 Electric Fracture and Fatigue

3.11 Summary

References

Chapter 4: Ferromagnetic Material Systems and Structures

Part 4.1 Ferromagnetics

4.1 Basic Equations of Magnetoelasticity

4.2 Magnetoelastic Instability

4.3 Magnetoelastic Vibrations and Waves

4.4 Magnetic Moment Intensity Factor

4.5 Tensile Fracture and Fatigue

4.6 Summary

Part 4.2 Magnetostriction

4.7 Basic Equations of Magnetostriction

4.8 Nonlinear Magneto-Mechanical Response

4.9 Magnetoelectric Response

4.10 Summary

References

Index

End User License Agreement

Pages

ix

xi

xiii

1

2

3

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

36

37

38

39

40

41

42

43

44

45

46

47

48

49

50

51

52

53

54

55

56

57

58

59

60

61

62

63

64

65

66

67

68

69

70

71

72

73

74

75

76

77

78

79

80

81

82

83

84

85

86

87

88

89

90

91

92

93

94

95

96

97

98

99

100

101

102

103

104

105

106

107

108

109

110

111

112

113

114

115

116

117

118

119

120

121

122

123

124

125

126

127

128

129

130

131

132

133

134

135

136

137

138

139

140

141

142

143

144

145

146

147

148

149

150

151

152

153

154

155

156

157

158

159

160

161

162

163

164

165

166

167

168

169

170

171

172

173

174

175

176

177

178

179

180

181

182

183

184

185

186

187

188

189

190

191

192

193

194

195

196

197

198

199

200

201

202

203

204

205

206

207

208

209

210

211

212

213

214

215

216

217

218

219

220

221

222

223

224

225

226

227

228

229

230

231

232

233

234

235

236

237

238

239

240

241

242

243

244

245

246

247

248

249

250

251

252

253

254

255

256

257

258

259

260

261

262

263

264

265

266

267

268

269

270

271

272

273

274

275

277

278

279

280

281

282

283

Guide

Cover

Table of Contents

Preface

Begin Reading

List of Illustrations

Chapter 2: Conducting Material Systems and Structures

Figure 2.1 Dynamic magnetoelastic interactions of conducting materials

Figure 2.2 An arbitrary material volume element

Figure 2.3 An electrically conducting elastic plate and magnetic flexural waves

Figure 2.4 Phase velocity versus wave number

Figure 2.5 Attenuation versus wave number

Figure 2.6 Phase velocity versus wave number

Figure 2.7 Attenuation versus wave number

Figure 2.8 Phase velocity versus wave number

Figure 2.9 Phase velocity versus wave number for Cases I, II, and III (perfect conductivity)

Figure 2.10 Phase velocity versus wave number (Mindlin plate, )

Figure 2.11 Phase velocity versus wave number (Mindlin plate, perfect conductivity)

Figure 2.12 Phase velocity versus wave number of the classical, Mindlin, and plane strain plates

Figure 2.13 Phase velocity versus wave number of the classical, Mindlin, and plane strain plates

Figure 2.14 Attenuation versus wave number of the classical, Mindlin, and plane strain plates

Figure 2.15 Phase velocity versus wave number of the classical, Mindlin, and plane strain plates (perfect conductivity)

Figure 2.16 A conducting plate with a through crack and incident waves

Figure 2.17 Dynamic bending moment intensity factor versus frequency of the Mindlin plate

Figure 2.18 Dynamic bending moment intensity factor versus magnetic field of the Mindlin plate

Figure 2.19 Dynamic bending moment intensity factor versus magnetic field of the Mindlin plate

Figure 2.20 Dynamic bending moment intensity factor versus frequency

Figure 2.21 A conducting plate with a through crack

Figure 2.22 Twisting moment intensity factor versus plate thickness to crack length ratio

Figure 2.23 Shear force intensity factor versus plate thickness to crack length ratio

Chapter 3: Dielectric/Ferroelectric Material Systems and Structures

Figure 3.1 Electroelastic interactions of dielectric materials

Figure 3.2 An infinite elastic dielectric material with a crack

Figure 3.3 Coordinate system used to express crack tip solutions

Figure 3.4 Typical contour for evaluation of path-independent line integral

Figure 3.5 Mode I electric stress intensity factor versus angle of loading

Figure 3.6 -integral versus angle of loading

Figure 3.7 Mode II electric stress intensity factor versus angle of loading

Figure 3.8 An elastic dielectric strip with a crack

Figure 3.9 Mode I electric stress intensity factor versus crack length to strip width ratio

Figure 3.10 Mode I electric stress intensity factor versus electric field

Figure 3.11 An elastic dielectric strip and electroelastic waves

Figure 3.12 Phase velocity of symmetric wave (Case I)

Figure 3.13 Phase velocity of antisymmetric wave (Case I)

Figure 3.14 Phase velocity of symmetric wave (Case II)

Figure 3.15 Phase velocity of antisymmetric waves (Case II)

Figure 3.16 An elastic dielectric material with a crack and incident waves

Figure 3.17 Mode I dynamic electric stress intensity factor versus electric field

Figure 3.18 Relations between the electrical and mechanical fields

Figure 3.19 Crystal structure of the perovskite ferroelectric

Figure 3.20 PZT Phase diagram

Figure 3.21 Polarization switching induced by electromechanical loads

Figure 3.22 Illustrations of grains in piezoelectric ceramics and basic unit of a crystallite with a displaceable domain wall

Figure 3.23 A laminated plate

Figure 3.24 Schematic drawing of (a) bimorph-type bending device and (b) multilayer stacked device

Figure 3.25 Schematic drawing of (a) inward series bimorph, (b) outward series bimorph, (c) parallel bimorph, and (d) unimorph or monomorph

Figure 3.26 A piezoelectric/metal/piezoelectric laminate

Figure 3.27 Schematic drawing of (a) cantilever beam and (b) simply supported beam

Figure 3.28 Flowchart of the FEA

Figure 3.29 A cantilever bimorph actuator and experimental setup

Figure 3.30 Tip deflection versus DC electric field

Figure 3.31 Tip deflection versus piezoelectric layer thickness

Figure 3.32 Tip deflection versus DC electric field under concentrated load

Figure 3.33 Tip deflection versus AC electric field

Figure 3.34 FGPM bimorphs

Figure 3.35 A 2 layer FGPM

Figure 3.36 FGPM property distributions

Figure 3.37 A clamped-free FGPM bimorph and experimental setup

Figure 3.38 Tip deflection versus AC voltage of the clamped-free FGPM bimorphs

Figure 3.39 Normal stress distribution along the thickness direction for the clamped-free FGPM bimorph

Figure 3.40 Shear stress distribution along the thickness direction for the clamped-free FGPM bimorph

Figure 3.41 Tip deflection and output voltage versus AC voltage of the clamped-free FGPM bimorphs

Figure 3.42 Tip deflection versus material volume fraction exponent of the clamped-free FGPM bimorphs

Figure 3.43 Output voltage versus material volume fraction exponent of the clamped-free FGPM bimorphs

Figure 3.44 Normal stress distribution along the thickness direction for the clamped-free FGPM bimorphs with different volume fraction exponents

Figure 3.45 A clamped–clamped FGPM bimorph and experimental setup

Figure 3.46 Sound pressure level versus frequency of the clamped–clamped FGPM bimorph

Figure 3.47 A hybrid laminated plate with sensor/actuator

Figure 3.48 Deflection along the length direction for the eight-layer graphite/epoxy laminate and nine-layer hybrid laminate

Figure 3.49 Cracking around an electrode tip

Figure 3.50 Two dissimilar piezoelectric half-planes with an internal electrode

Figure 3.51 A piezoelectric half-plane with a surface electrode

Figure 3.52 Normal stress distribution along the -direction for the P-7/P-7 laminates

Figure 3.53 Unit cell of multilayer piezoelectric actuators

Figure 3.54 A four-layer piezoelectric actuator

Figure 3.55 A four-layer actuator and experimental setup

Figure 3.56 Finite element model of the four-layer piezoelectric actuator

Figure 3.57 Normal strain distribution along the -direction for the four-layer piezoelectric actuator

Figure 3.58 Normal strain versus DC electric field of the four-layer piezoelectric actuator

Figure 3.59 Typical model of the four-layer unpoled piezoelectric actuator

Figure 3.60 Displacement versus DC electric field of the four-layer unpoled piezoelectric actuator

Figure 3.61 Images of poling for the four-layer piezoelectric actuator under at (a) , (b) , and (c)

Figure 3.62 Images of poling for the four-layer piezoelectric actuator under at (a) , (b) , and (c)

Figure 3.63 Two dissimilar piezoelectric half-spaces with an internal circular electrode

Figure 3.64 A piezoelectric half-space with a surface circular electrode

Figure 3.65 A piezoelectric disk composite with circular electrodes

Figure 3.66 Strain versus DC electric field of the piezoelectric disk composite

Figure 3.67 A piezoelectric circular plate with circular electrodes

Figure 3.68 Sketch of (a) 1–3 composite, (b) AFC, and (c) MFC

Figure 3.69 Finite element model of the 1–3 piezocomposite with (a) square and (b) circular PZT rods

Figure 3.70 A 1–3 piezocomposite

Figure 3.71 Displacement versus DC electric field of the 1–3 piezocomposites

Figure 3.72 Images of polarization switching for the 1–3 piezocomposites under MV/m

Figure 3.73 Electrical impedance spectra of the 1–3 piezocomposites

Figure 3.74 Schematic drawing of (a) lay-up and geometry and (b) repeating unit of MFC

Figure 3.75 Image of poling for the partially poled PZT fiber

Figure 3.76 A M-4010-P1-type MFC

Figure 3.77 Strain versus DC electric field of the MFC

Figure 3.78 Schematic drawing of mirror device

Figure 3.79 A mirror device

Figure 3.80 Mirror tilt angle

Figure 3.81 Tilt angle versus DC electric field of the mirror device

Figure 3.82 Normal stress distribution along the length direction for PZT thick film

Figure 3.83 Analytical and experimental phase diagrams of PZT

Figure 3.84 Piezoelectric coefficients of PZT-4 from room to cryogenic temperatures

Figure 3.85 A piezoelectric stacked actuator and experimental setup at cryogenic temperatures

Figure 3.86 Normal strain versus temperature of the piezoelectric stacked actuator (cryogenic temperature range)

Figure 3.87 Normal strain versus DC electric field of the piezoelectric stacked actuator

Figure 3.88 Normal strain versus AC electric field of the piezoelectric stacked actuator at liquid hydrogen temperature

Figure 3.89 Normal strain and electric field distributions along the -direction for the piezoelectric stacked actuator at liquid hydrogen temperature

Figure 3.90 Image of depolarization

Figure 3.91 A piezoelectric stacked actuator and experimental setup at high temperatures

Figure 3.92 Normal strain versus temperature of the piezoelectric stacked actuator (high temperature range)

Figure 3.93 Normal strain versus DC electric field of the piezoelectric stacked actuator at high temperatures

Figure 3.94 Two piezoelectric half-planes

Figure 3.95 Normal strain versus distance of the two piezoelectric half-planes

Figure 3.96 Electric field versus distance of the two piezoelectric half-planes

Figure 3.97 An infinite piezoelectric material with an elliptic hole

Figure 3.98 An infinite piezoelectric material with a plane strain crack: (a) Case 1, (b) Case 2

Figure 3.99 Sketch of piezoelectric strip with a central crack: (a) Case 1, (b) Case 2

Figure 3.100 Indentation crack in piezoelectric ceramics

Figure 3.101 Sketch of piezoelectric strip containing a central crack with two postulated yield zones

Figure 3.102 Sketch of (a) cracked piezoelectric strip, (b) cracked piezoelectric strip bonded between two elastic half-planes, and (c) cracked piezoelectric strip bonded between two piezoelectric half-planes

Figure 3.103 An infinite piezoelectric material with a penny-shaped crack

Figure 3.104 Sketch of (a) cracked piezoelectric cylinder and (b) cracked piezoelectric fiber embedded in an elastic matrix

Figure 3.105 An infinite piezoelectric material with an antiplane shear crack

Figure 3.106 Sketch of (a) piezoelectric strip with a crack parallel to the edges of the strip, (b) piezoelectric strip with a crack normal to the edges of the strip, and (c) piezoelectric laminate with an interface crack

Figure 3.107 Sketch of (a) cracked piezoelectric material, (b) cracked piezoelectric laminate, and (c) arc-shaped interface cracks between a piezoelectric fiber and a polymer matrix

Figure 3.108 A symmetric thermopiezoelectric laminated plate with a through crack

Figure 3.109 Sketch of symmetric piezoelectric laminated plate with a through crack

Figure 3.110 A rectangular piezoelectric material with a central crack normal to the poling and electric field

Figure 3.111 Typical contours and for the evaluation of path-independent line integral

Figure 3.112 Finite element mesh and paths of -integral

Figure 3.113 Contribution from the crack interior versus critical electric field level for discharge

Figure 3.114 Energy release rate versus electric field of the rectangular piezoelectric material under applied displacement (permeable crack model)

Figure 3.115 Energy release rate versus electric field of the rectangular piezoelectric material under applied displacement (permeable, impermeable, open, and discharging crack models)

Figure 3.116 Energy release rate versus negative electric field of the rectangular piezoelectric material under applied displacement (permeable crack model)

Figure 3.117 Energy release rate versus electric field of the rectangular piezoelectric material under applied stress (permeable and impermeable crack models)

Figure 3.118 Energy release rate versus electric field of the rectangular piezoelectric material under high applied stress (permeable and impermeable crack models)

Figure 3.119 A rectangular piezoelectric material with a central crack parallel to the poling and electric field

Figure 3.120 Energy release rate versus electric field of the rectangular piezoelectric material under applied displacement (permeable and impermeable crack models)

Figure 3.121 A rectangular piezoelectric material with an edge crack normal to the poling and electric field

Figure 3.122 Geometry and boundary conditions of the DCB

Figure 3.123 Finite element mesh of the DCB with end block and paths of -integral

Figure 3.124 Energy release rate versus electric field of the DCB piezoelectric material under applied load (permeable, impermeable, open, and discharging crack models)

Figure 3.125 Energy release rate versus electric field of the DCB piezoelectric material under high applied load (impermeable crack model)

Figure 3.126 Images of dielectric breakdown region near (a) permeable and (b) impermeable cracks induced by tensile load and high positive electric field

Figure 3.127 IF test setup

Figure 3.128 Crack length versus electric field of the IF specimen

Figure 3.129 Apparent fracture toughness versus electric field of the IF specimen

Figure 3.130 Finite element model of the IF test

Figure 3.131 Energy release rate versus electric field of the IF specimen

Figure 3.132 MSP test setup

Figure 3.133 Finite element model of the MSP test

Figure 3.134 Fracture initiation load versus electric field of the MSP specimen

Figure 3.135 Fracture surfaces of the MSP specimen under (a) MV/m and (b) MV/m

Figure 3.136 Load–displacement curves of the MSP specimen

Figure 3.137 Critical MSP energy versus electric field of the MSP specimen

Figure 3.138 Image of polarization switching for the MSP specimen under N and MV/m

Figure 3.139 SEPB Specimen

Figure 3.140 Schematic drawing of precracking technique

Figure 3.141 SEPB test setup

Figure 3.142 Finite element model of the SEPB test

Figure 3.143 Fracture load versus crack length to specimen width ratio of the SEPB specimen

Figure 3.144 Fracture load and critical energy release rate versus electric field of the SEPB specimen

Figure 3.145 Energy release rate versus electric field of the SEPB specimen

Figure 3.146 Partially poled SEPB specimen

Figure 3.147 SEPB setup at 77 K

Figure 3.148 Finite element model of the partially poled SEPB test

Figure 3.149 Fracture appearances of the SEPB specimen under V/m at (a) RT and (b) 77 K

Figure 3.150 Fracture surfaces of the SEPB specimen under MV/m at (a) RT and (b) 77 K

Figure 3.151 Energy release rate versus temperature of the SEPB specimen

Figure 3.152 DT specimen

Figure 3.153 Energy release rate versus crack length of the DT specimen

Figure 3.154 Fracture surfaces (a) near the precrack tip and (b) away from the precrack tip of the SEPB specimen under MV/m

Figure 3.155 Fracture surfaces (a) near the precrack tip and (b) away from the precrack tip of the SEPB specimen under MV/m

Figure 3.156 Energy release rate versus AC electric field of the SEPB specimen

Figure 3.157 Energy release rate versus time-to-failure of the SEPB specimen

Figure 3.158 Fracture load versus load rate of the SEPB specimen

Figure 3.159 Crack propagation velocity versus energy release rate of the SEPB specimen

Figure 3.160 Fatigue crack growth rate versus maximum energy release rate of the SEPB specimen

Figure 3.161 Maximum energy release rate versus number of cycles to failure of the SEPB specimen

Chapter 4: Ferromagnetic Material Systems and Structures

Figure 4.1 Magnetoelastic interactions of ferromagnetic materials

Figure 4.2 A ferromagnetic plate

Figure 4.3 A cantilever ferromagnetic plate

Figure 4.4 Deflection versus magnetic field

Figure 4.5 A ferromagnetic plate and magnetic flexural waves

Figure 4.6 Phase velocity versus wave number of the classical plate

Figure 4.7 Phase velocity versus wave number of the classical, Mindlin, and plane strain plates

Figure 4.8 A simply supported soft ferromagnetic plate with a through crack

Figure 4.9 A fixed-end soft ferromagnetic plate with a through crack

Figure 4.10 Position of strain gage and coordinate system used to express crack tip strain

Figure 4.11 Moment intensity factor versus magnetic field

Figure 4.12 A soft ferromagnetic plate with a through crack and incident waves

Figure 4.13 A rectangular soft ferromagnetic material with a central crack

Figure 4.14 Stress intensity factor versus strip width to crack length ratio

Figure 4.15 Stress intensity factor versus magnetic field

Figure 4.16 Single-edge cracked specimen

Figure 4.17 Fracture toughness test setup

Figure 4.18 Fatigue crack growth rate versus stress intensity factor range

Figure 4.19 Magnetostriction

Figure 4.20 A Terfenol-D/metal laminate

Figure 4.21 Various deformation modes

Figure 4.22 Schematic diagram of (a) strain versus magnetic field curve and (b) domain structure

Figure 4.23 Tip deflection versus magnetic field

Figure 4.24 A Terfenol-D/PZT laminate

Figure 4.25 Illustration of a Terfenol-D/PZT laminate under (a) magnetic field, (b) AC electric field, and (c) concentrated mechanical loading

List of Tables

Chapter 2: Conducting Material Systems and Structures

Table 2.1 Phase velocity and attenuation versus wave number for Cases I, II, and III (quasistatic electromagnetic field)

Chapter 3: Dielectric/Ferroelectric Material Systems and Structures

Table 3.1 Sound pressure level of the clamped–clamped FGPM bimorphs

Table 3.2 Output voltage of the clamped–clamped FGPM bimorphs

Table 3.3 Fundamental resonance frequency of the mirror device

Table 3.4 Comparison of energy release rates for four crack models

Table 3.5 Comparison of energy release rates at the midwidth for four crack models

Table 3.6 Comparison of energy release rates for four crack models of the SEPB specimen

Table 3.7 Fracture loads of the SEPB specimen at RT and 77 K

Table 3.8 Fracture loads of the DT specimens

Table 3.9 Times-to-failure of the SEPB specimens under DC electric field

Table 3.10 Times-to-failure of the SEPB specimens under AC electric field

Table 3.11 Fracture loads of the SEPB specimens under AC electric field

Table 3.12 Critical energy release rates of the SEPB specimens under AC electric field

Chapter 4: Ferromagnetic Material Systems and Structures

Table 4.1 Critical buckling magnetic induction

Table 4.2 Fracture loads of the single-edge cracked specimens under the magnetic field

Table 4.3 Fracture toughnesses of the single-edge cracked specimens under the magnetic field

Table 4.4 Second-order magnetoelastic constants

ELECTROMAGNETO-MECHANICS OF MATERIAL SYSTEMS AND STRUCTURES

Yasuhide Shindo

Tohoku University, Japan

This edition first published 2015

© 2015 John Wiley & Sons Singapore Pte. Ltd.

Registered office

John Wiley & Sons Singapore Pte. Ltd., 1 Fusionopolis Walk, #07-01 Solaris South Tower, Singapore 138628.

For details of our global editorial offices, for customer services and for information about how to apply for permission to reuse the copyright material in this book please see our website at www.wiley.com.

All Rights Reserved. No part of this publication may be reproduced, stored in a retrieval system or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording, scanning, or otherwise, except as expressly permitted by law, without either the prior written permission of the Publisher, or authorization through payment of the appropriate photocopy fee to the Copyright Clearance Center. Requests for permission should be addressed to the Publisher, John Wiley & Sons Singapore Pte. Ltd., 1 Fusionopolis Walk, #07-01 Solaris South Tower, Singapore 138628, tel: [phone], fax: [phone], email: [email protected].

Wiley also publishes its books in a variety of electronic formats. Some content that appears in print may not be available in electronic books.

Designations used by companies to distinguish their products are often claimed as trademarks. All brand names and product names used in this book are trade names, service marks, trademarks or registered trademarks of their respective owners. The Publisher is not associated with any product or vendor mentioned in this book. This publication is designed to provide accurate and authoritative information in regard to the subject matter covered. It is sold on the understanding that the Publisher is not engaged in rendering professional services. If professional advice or other expert assistance is required, the services of a competent professional should be sought.

Limit of Liability/Disclaimer of Warranty: While the publisher and author have used their best efforts in preparing this book, they make no representations or warranties with respect to the accuracy or completeness of the contents of this book and specifically disclaim any implied warranties of merchantability or fitness for a particular purpose. It is sold on the understanding that the publisher is not engaged in rendering professional services and neither the publisher nor the author shall be liable for damages arising herefrom. If professional advice or other expert assistance is required, the services of a competent professional should be sought.

Library of Congress Cataloging-in-Publication Data applied for.

ISBN: 9781118837962

About the Author

Dr. Shindo received his Doctorate of Engineering from Tohoku University in 1977. He is currently a professor in the Department of Materials Processing in the Graduate School of Engineering at Tohoku University. Dr. Shindo also served on the Board of Editors of the International Journal of Solids and Structures and is currently serving on the editorial board of Journal of Mechanics of Materials and Structures, the Advisory Board of Acta Mechanica, the International Editorial Board of AES Technical Reviews International Journal (Part A: International Journal of Nano and Advanced Engineering Materials (IJNAEM), Part B: International Journal of Advances in Mechanics and Applications of Industrial Materials (IJAMAIM), Part C: International Journal of Advances and Trends in Engineering Materials and their Applications (IJATEMA), Part D: International Journal of Reliability and Safety of Engineering Systems and Structures (IJRSESS)), the Editorial Advisory Board of The Open Civil Engineering Journal/The Open Textile Journal/The Open Conference Proceeding Journal/The Open Physics Journal (formerly The Open Mechanics Journal), the Editorial Board of Advances in Theoretical and Applied Mechanics, Chemical Engineering and Process Techniques, International Scholarly Research Notices (Mechanical Engineering), Journal of Applied Mathematics, the editorial board of Strength, Fracture and Complexity, An International Journal, and the Editor-in-Chief of The Open Mechanical Engineering Journal and International Journal of Metallurgical & Materials Engineering. His primary research interests are in the areas of mesomechanics of material systems and structures, electromagnetic fracture and damage mechanics, dynamics and cryomechanics of advanced composite materials/structural alloys, and reliability and durability of micro-/nanocomponents and devices.

Preface

The science of electromagneto-mechanics, which is concerned with the interaction of electromagnetic fields and deformation in material systems and structures, has developed because of the possibility of its practical applications in various fields such as electronic and electromechanical devices. As the area of science and technology expands, it becomes important that newly acquired knowledge and expertise are communicated effectively to those who can gain most by applying them in practice. This book covers a very wide and varied range of subject areas that fall under its subject and all aspects (theoretical, experimental, computational studies, and/or industrial applications) of electromagneto-mechanics from state-of-the-art fundamental research to applied research and applications in emerging technologies.

Yasuhide Shindo

Sendai, JapanSeptember, 2014

Acknowledgments

I am indebted to many authors whose writings are classics in the field of electromagneto-mechanics. It is also a pleasure to acknowledge the help received from my students and colleagues. Special thanks go to Professor Fumio Narita of Tohoku University, who read the entire manuscript and gave me many valuable suggestions for improvement. Finally, I would like to thank the publisher John Wiley & Sons for their continuous support for this project.

Chapter 1Introduction

The electromagneto-mechanics of material systems and structures has been developing rapidly with extensive applications in, for example, electronic industry, magnetic fusion engineering, superconducting devices, and smart materials and microelectromechanical systems (MEMS). Researchers in this interdisciplinary field are with diverse background and motivation. This book reflects a cross section of recent activities in the electromagneto-mechanics of conducting materials, dielectric materials, piezoelectric materials and devices, ferromagnetic materials, magnetostrictive material systems, and so on.

Chapter 2 deals with the magneto-mechanics of conducting material systems and structures. Here, the theory of dynamic magnetoelasticity is presented. Vibrations and waves of conducting plates are then considered, and the effect of the magnetic field on the flexural waves is examined. The theory is also applied to various problems for cracked conducting plates, and the influence of the magnetic field on the dynamic singular stresses is displayed graphically and discussed. In addition, the results for the cracked plates under large electric current and strong magnetic field are presented, and the effect of the electromagnetic force on the mechanical behavior is shown.

Chapter 3 provides the electromechanical interactions of dielectric/ferroelectric material systems and structures. In Part 3.1, we present the theory of dielectrics. Basic equations of electroelasticity are given. Applications are then made to static electroelastic crack mechanics, electroelastic vibrations and waves, and dynamic electroelastic crack mechanics of dielectric materials. Part 3.2 is devoted to the discussion of linear and nonlinear piezoelectricity. For a literature on this topic, we refer readers to Tiersten 1. Piezomechanics and basic equations are presented. Theory is then applied to various problems, including bending behavior, electromechanical field concentrations, and cryogenic electromechanical response. Experimental data are also shown to validate the theoretical model. Furthermore, the theoretical and experimental results on the electric field dependence of fracture and fatigue of piezoelectric material systems are presented.

In Chapter 4, we deal with the magneto-mechanics of ferromagnetic material systems and structures. Part 4.1 presents the theory and test of ferromagnetics. Reference on this topic may be made to Brown 2. Basic equations of magnetoelasticity are developed. Theory is then applied to various problems, including magnetoelastic instability, magnetoelastic vibrations, and waves of soft ferromagnetic and magnetically saturated materials under magnetic fields, and some experiments are performed to validate the theoretical predictions. The magnetoelastic analysis and experimental evidence are also presented for cracked plates under bending, and the effect of magnetic fields on the moment intensity factor is shown. Moreover, the tensile fracture and fatigue of soft ferromagnetic materials under magnetic fields are dedicated. Part 4.2 is concerned with a discussion of magnetostriction. Works on the subject are found to be in du Tremolet de Lacheisserie 3. Basic equations of magnetostriction are given. Theoretical and experimental treatments of the nonlinear magneto-mechanical response in magnetostrictive material systems are then presented. Here, the material systems consist of the magnetostrictive and elastic layers, and later, we consider the magnetostrictive layer bonded to the piezoelectric layer. In addition, the piezomagnetoelectric effect of particle-reinforced composites is discussed.

There are extensive literatures on this subject. Some books are listed as follows. That is, Moon 4 organized the existing literatures on magneto-solid mechanics and gave a presentation of the basic principles and some useful method of analysis. Parton and Kudryavtsev 5 analyzed the behavior of piezoelectric materials and considered strength and failure problems for piezoelectric and electrically conducting materials. In addition, Eringen and Maugin 6, 7 presented a unified approach to the nonlinear continuum theory of deformable and fluent materials subjected to electromagnetic and thermal loads. Also, there are the following conference proceedings books of IUTAM symposium: Maugin 8, Yamamoto and Miya 9, and Hsieh 10, and of other mini-symposiums: Lee et al. 11, Yang and Maugin 12, and Shindo 13. Moreover, the following monographs present a good discussion of this subject: Paria 14, Parkus 15, 16, Alblas 17, Moon 18, Hutter and van de Ven 19, Pao 20, Hsieh 21, Ambartsumian 22, and the set of chapters edited by Parkus 23. In the above-listed literatures, references to other papers can be found.

References

[1] H. F. Tiersten,

Linear Piezoelectric Plate Vibration

, Plenum Press, New York, 1969.

[2] W. F. Brown, Jr.,

Magnetoelastic Interactions

, Springer-Verlag, Berlin, 1966.

[3] E. du Tremolet de Lacheisserie,

Magnetostriction: Theory and Applications of Magnetoelasticity

, CRC Press, Boca Raton, FL, 1993.

[4] F. C. Moon,

Magneto-Solid Mechanics

, John Wiley & Sons, Inc., New York, 1984.

[5] V. Z. Parton and B. A. Kudryavtsev,

Electromagnetoelasticity

, Gordon and Breach Science Publishers, New York, 1988.

[6] A. C. Eringen and G. A. Maugin,

Electrodynamics of Continua I

, Springer-Verlag, New York, 1989.

[7] A. C. Eringen and G. A. Maugin,

Electrodynamics of Continua II

, Springer-Verlag, New York, 1990.

[8] G. A. Maugin (ed.),

Proceedings of the IUTAM/IUPAP Symposium on the Mechanical Behavior of Electromagnetic Solid Continua

, North-Holland, Amsterdam, 1984.

[9] Y. Yamamoto and K. Miya (eds.),

Proceedings of the IUTAM Symposium on Electromagnetomechanical Interactions in Deformable Solids and Structures

, North-Holland, Amsterdam, 1987.

[10] R. K. T. Hsieh (ed.),

Proceedings of the IUTAM Symposium on Mechanical Modeling of New Electromagnetic Materials

, Elsevier, Amsterdam, 1990.

[11] J. S. Lee, G. A. Maugin and Y. Shindo (eds.),

Mechanics of Electromagnetic Materials and Structures

, AMD-Vol. 161, MD-Vol. 42, ASME, New York, 1993.

[12] J. S. Yang and G. A. Maugin (eds.),

Mechanics of Electromagnetic Materials and Structures

, IOS Press, Amsterdam, 2000.

[13] Y. Shindo (ed.),

Mechanics of Electromagnetic Material Systems and Structures

, WIT Press, Southampton, 2003.

[14] G. Paria, “Magneto-elasticity and magneto-thermo-elasticity,”

Adv. Appl. Mech.

10

, 73 (1967).

[15] H. Parkus, “Variational principles in thermo- and magneto-elasticity,”

CISM Courses and Lectures

Vol.

58

, Springer-Verlag, Wien, 1970.

[16] H. Parkus, “Magneto-thermoelasticity,”

CISM Courses and Lectures

Vol.

118

, Springer-Verlag, Wien, 1972.

[17] J. B. Alblas, “Electro-magneto-elasticity,”

Topics in Applied Continuum Mechanics

, J. L. Zeman and F. Ziegler (eds.), Springer-Verlag, Wien, p. 71 (1974).

[18] F. C. Moon, “Problems in magneto-solid mechanics,”

Mech. Today

4

, 307 (1978).

[19] K. Hutter and A. A. F. van de Ven, “Field matter interactions in thermoelastic solids: a unification of existing theories of electro-magneto-mechanical interactions,”

Lecture Notes in Physics

Vol.

88

, Springer-Verlag, Berlin, 1978.

[20] Y.-H. Pao, “Electromagnetic forces in deformable continua,”

Mech. Today

4

, 209 (1978).

[21] R. K. T. Hsieh, “Micropolarized and magnetized media,”

Mechanics of Micropolar Media

, O. Brulin and R. K. T. Hsieh (eds.), World Scientific, Singapore, p. 187 (1982).

[22] S. A. Ambartsumian, “Magneto-elasticity of thin plates and shells,”

Appl. Mech. Rev.

35

(1), 1 (1982).

[23] H. Parkus (ed.), “Electromagnetic interactions in elastic solids,”

CISM Courses and Lectures

Vol.

257

, Springer-Verlag, Wien, 1979.

Chapter 2Conducting Material Systems and Structures

If electrically conducting materials are used in strong magnetic field, we must consider the effect of induced current. Figure 2.1 shows the dynamic magnetoelastic interactions of conducting materials. In this chapter, first, magnetoelastic vibrations and waves of conducting materials are discussed. Next, the influence of magnetic field on the dynamic singular stresses in cracked conducting materials is described.

The components of the superconducting structures are most often used in environments with large electric currents and strong magnetic fields. The singular stresses in cracked conducting materials under electromagnetic force are also examined in this chapter.

Figure 2.1 Dynamic magnetoelastic interactions of conducting materials

2.1 Basic Equations of Dynamic Magnetoelasticity

Let us now consider the rectangular Cartesian coordinates . Electrically conducting materials are permeated by a static uniform magnetic field