Handbook of micromechanics and nanomechanics

1256 Pages·2013·31.95 MB·English

by  Shaofan Li, Xin-Lin Gao

“This book represents an extensive collection of state-of-the-art studies on
micromechanics and nanomechanics. It is a very comprehensive text covering a wide M
range of theories and numerical and experimental methods, and it has applications
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to many important classes of materials and structures.” C
Prof. Yonggang Huang R
Northwestern University, USA O
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“I found the depth in the mechanics remarkable, extending to such topics as solutions
to the periodic Eshelby inclusion problem. Overall, there is a balance of theory E
and applications, and it will be most useful for researchers and developers of new C
technologies.” H
Prof. Xanthippi Markenscoff A
University of California, San Diego, USA NH
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“This handbook, written by leaders in their various fields, presents snapshots of C
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recent advances in the fields of micromechanics and nanomechanics through 30 well- S
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written chapters. This reviewer is impressed by the scope of the materials presented
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and the careful writing that covers these advanced topics.”
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Prof. Leon M. Keer
DO
Northwestern University, USA
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This book presents the latest developments in micromechanics and nanomechanics and
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their applications. Particularly, it focuses on some recent applications and impact areas of
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micromechanics and nanomechanics that have not been discussed in traditional books on
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this subject. The text covers analytical, experimental, and computational and numerical
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approaches in depth. It presents some latest research developments systematically HANDBOOK OF
disseminated in the form of a review volume. The book explores the connection between E
micromechanics and nanomechanics and does not treat them as separate scientific C
subjects. Readers can therefore see and understand the underlying physics from a far H
broader perspective than the traditional engineering mechanics approach can provide. A MICROMECHANICS

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Shaofan Li is a professor of applied and computational mechanics in the I
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Department of Civil and Environmental Engineering at the University
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of California—Berkeley. He has published more than 100 technical
papers in peer-reviewed archival journals in the field of micromechanics
A NANOMECHANICS

and computational mechanics. Dr. Li is also the author of two research
monographs, including the graduate textbook, Introduction to Micromechanics and N
Nanomechanics.
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Xin-Lin Gao is a professor of mechanical engineering, bioengineering, a L
and materials science and engineering at the University of Texas at Dallas. o i
Shaofan Li and Xin-Lin Gao
He also serves on four technical committees in three divisions (Applied edited by
Mechanics, Materials, Aerospace) of ASME. Dr. Gao has been a guest chair
professor at East China University of Science and Technology since 2010.
He served as the chair of the ASME/Boeing Structures and Materials Best Paper Award
Committee in 2006 and 2007. He was elected an ASME fellow in 2011.
V344
ISBN 978-981-441-12-33
HANDBOOK OF
MICROMECHANICS

ANANOMECHANICS
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© 2013 by Taylor & Francis Group, LLC
© 2013 by Taylor & Francis Group, LLC
HANDBOOK OF
MICROMECHANICS

ANANOMECHANICS
N
D
edited by Shaofan Li and Xin-Lin Gao
© 2013 by Taylor & Francis Group, LLC
CRC Press
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© 2013 by Taylor & Francis Group, LLC
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Version Date: 20130410
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© 2013 by Taylor & Francis Group, LLC
March4,2013 10:48 PSPBook-9inx6in 00-Shaofan-Li–prelims
Contents

Preface xxv
1 MicrodynamicsofPhononicMaterials 1

Mahmoud I. Hussein, Michael J. Frazier,
and Mohammad H. Abedinnasab
1.1 Introduction 1

1.2 WavePropagationin1DPhononicMaterials 2

1.2.1 Background 2

1.2.2 TransferMatrixMethod 4

1.3 TreatmentofDamping 8

1.3.1 ViscouslyDampedWavesin1DHomogeneous

Media 9

1.3.2 ViscouslyDampedWavesin1DPhononic

Materials 11

1.4 TreatmentofNonlinearity 14

1.4.1 FiniteStrainWavesin1DHomogenousMedia 15

1.4.1.1 Equationofmotion 16

1.4.1.2 Dispersionrelation 18

1.4.2 FiniteStrainWavesin1DPhononicMaterials 21

2 MicromechanicsofElasticMetamaterials 29

Xiaoming Zhou, Xiaoning Liu, Gengkai Hu,
and Guoliang Huang
2.1 Introduction 29

2.2 DiscreteMass–SpringModelofMetamaterials 32

2.2.1 NegativeEffectiveMass 32

2.2.2 NegativeEffectiveModulus 38

2.3 ContinuumMaterialModelofMetamaterials 40

2.3.1 CompositeswithCoatedSphereInclusions 40

2.3.2 ChiralMetamaterials 48

© 2013 by Taylor & Francis Group, LLC
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vi Contents
2.4 ApplicationsofElasticMetamaterials 52

2.4.1 CloakinginQuasi-StaticApproximation 52

2.4.2 TransformationAcousticsandElasticity 57

2.4.3 AcousticImagingbeyondtheDiffraction

Limit 62

2.5 Conclusions 66

3 PhaseFieldApproachandMicromechanicsinFerroelectric

Crystals 73

Yu Su and George J. Weng
3.1 Introduction 74

3.2 TheFundamentalsofPhaseFieldApproach 75

3.2.1 FreeEnergyandtheConstitutiveRelations 76

3.2.2 TheKineticsofNon-EquilibriumProcess 84

3.3 ApplicationsofPhaseFieldApproach 88

3.3.1 ApplicationsinFerroelectricBulkSingle

Crystals 89

3.3.2 ApplicationsinFerroelectricBulkPolycrystals 94

3.3.3 ApplicationsinFerroelectricThinFilms 96

3.3.4 ApplicationsinFerroelectricLowDimensional

Structures 101

3.4 TheFundamentalsofMicromechanicsApproach 104

3.4.1 ConstitutiveRelations 105

3.4.2 GibbsFreeEnergyforPhaseTransitionand

DomainSwitch 108

3.4.3 ThermodynamicDrivingForce 112

3.4.4 KineticEquations 115

3.4.5 TheOverallElectromechanicalResponse 118

3.5 ApplicationsofMicromechanicsApproach 118

3.5.1 NonlinearStress–Strainand

Stress–DepolarizationRelationsofaPoledPZT

underCompression 119

3.5.2 TheShiftofCurieTemperatureunder

HydrostaticPressure 119

3.5.3 HysteresisandButterfly-ShapedAxialStrain

vs.ElectricFieldRelations 120

3.5.4 DoubleHysteresisofaFerroelectricCrystal

AboveT 121

C
© 2013 by Taylor & Francis Group, LLC
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Contents vii
3.5.5 TripleHysteresisandtheAssociatedDielectric
ConstantsofBaTiO Near5◦C 122
3
3.5.6 DevelopmentofRank-1andRank-2Domain

Pattern,andInfluenceofaCompressiveStress

inBaTiO 124

3
3.6 ConcludingRemarks 127

Appendix:TheCoefficientsinEquation(3.24) 129

4 AtomicStructureofFerroelectric180◦ DomainWallsin

PbTiO 141

3
Arash Yavari and Arzhang Angoshtari

4.1 Introduction 141

4.2 Geometryof180◦ DomainWalls 148

4.2.1 PerfectDomainWalls 149

4.2.2 DomainWallswithPointDefects 149

4.2.3 StepsinDomainWalls 150

4.3 AnalyticLatticeModels 152

4.3.1 TheEnsembleTheories 152

4.3.1.1 MicroCanonicalEnsembleTheory 152

4.3.1.2 CanonicalEnsembleTheory 153

4.3.2 ShellPotentials 154

4.3.3 LatticeStatics 157

4.3.3.1 DefectiveCrystalsandSymmetry

Reduction 158

4.3.3.2 HessianMatrixfortheBulkCrystal 160

4.3.4 Quasi-HarmonicLatticeDynamics 161

4.3.4.1 Finitesystems 161

4.3.4.2 Perfectcrystals 164

4.3.4.3 Latticeswithmasslessparticles 167

4.3.4.4 DefectiveCrystals 170

4.3.5 Quasi-NewtonMethod 173

4.4 AtomicStructureof180◦ DomainWalls 175
4.4.1 NormalandShearStrains 175
4.4.1.1 Perfectdomainwalls 176
4.4.1.2 DomainWallswithOxygenVacancies 179

4.4.2 StepsinDomainWalls 182
4.4.2.1 Pb–Pbsteps 183
4.4.2.2 Ti–Tisteps 187
© 2013 by Taylor & Francis Group, LLC
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viii Contents
4.4.2.3 Pb–TiSteps 187

4.4.3 ExternalElectricFields 188

4.4.3.1 Perfectdomainwalls 191

4.4.3.2 Defectivedomainwalls 194

4.4.4 Temperature 196

5 Micromechanics-BasedConstitutiveModelingof

Chain-StructuredFerromagneticParticulateComposites 211

Huiming Yin, Lizhi Sun, and Hua Zhang

5.1 Introduction 212

5.2 FundamentalSolutiontoMagneto-ElasticProblems 215

5.2.1 ModifiedMagneticGreen’sFunctions 216

5.2.2 ModifiedElasticGreen’sFunctionsConsidering

BodyForce 218

5.2.3 ModifiedElasticGreen’sFunctionsConsidering

Eigenstrain 220

5.2.4 SolutionsforTwoSpheresintheInfinite

Medium 222

5.2.4.1 Magnetostaticfield 222

5.2.4.2 Magneticforcebetweenparticles 225

5.2.4.3 Elasticfield 227

5.3 Magneto-ElasticConstitutiveModelingon

Chain-StructuredFerromagneticParticulate

Composites 228

5.3.1 MagneticBehaviorofMagneticComposites 228

5.3.2 Magneto-ElasticBehaviorofFerromagnetic

Composites 232

5.4 ResultsandDiscussion 238

5.5 Conclusions 247

6 DynamicElectromechanicsinFunctionallyGraded

PiezoelectricMaterials 255

Yasuhide Shindo and Fumio Narita

6.1 Introduction 255

6.2 Analysis 256

6.2.1 BasicEquations 256

6.2.2 DomianWallMotion 258

6.2.3 FunctionalGrading 261

6.2.4 FiniteElementModel 262

© 2013 by Taylor & Francis Group, LLC
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Contents ix
6.3 Experiment 263
6.3.1 MaterialandSpecimenPreparation 263
6.3.2 Clamped-FreeFGPMPlates 264
6.3.3 Clamped-ClampedFGPMPlates 265
6.4 ResultsandDiscussion 266
6.4.1 ResultsofClamped-FreeBimorphs 266
6.4.2 ResultsofClamped-ClampedBimorphs 268

6.5 Conclusions 270

7 Mechano-ElectrochemicalMixtureTheoriesforthe

MultiphaseFluidInfiltratedPoroelasticMedia 273

Hamed Hatami-Marbini

7.1 Introduction 273

7.2 PreliminaryDefinitions 280

7.3 MixtureKinematics 282

7.4 BalancePrinciples 284

7.4.1 ConservationofMass 284

7.4.2 Electro-NeutralityCondition 286

7.4.3 ConservationofMomentum 286

7.5 EntropyPrincipleandConstitutiveRelations 288

7.6 DeformationDependentSolutefluxRelations 293

7.7 Summary 295

8 MicromechanicsofNanocompositeswithInterfaceEnergy

Effect 303

Zhuping Huang and Jianxiang Wang

8.1 Introduction 304

8.2 FundamentalEquationsoftheInterfaceatFinite

Deformation 307

8.2.1 GeometryofaDeformableInterface/Surface 307

8.2.2 ConstitutiveRelationsoftheInterfaceatFinite

Deformation 311

8.2.3 The“ThreeConfigurations”Concept 313
8.2.4 TheLagrangianandEulerianDescriptionsof
InterfaceEquilibriumEquations 318
8.3 InfinitesimalStrainAnalysis 323
8.3.1 TheInfinitesimalInterfaceStrain 323
8.3.2 ConstitutiveRelationsoftheInterface 324
© 2013 by Taylor & Francis Group, LLC