Micromechanics and Nanomechanics of Composite Solids (eBook)

Dr. Shaker A. Meguid is Professor and Director, Mechanics and Aerospace Design Laboratory, University of Toronto, Ontario, CANADA. Dr. George J. Weng is Distinguished Professor, Department of Mechanical & Aerospace Engineering, Rutgers University, New Jersey  USA.

Preface 5
Contents 8
Contributors 10
1 Sequential and Concurrent Multiscale Modeling of Multiphysics: From Atoms to Continuum 13
1.1 Introduction 14
1.2 Molecular Dynamics Simulation of Multiphysics 15
1.2.1 Reformulation of Nosé-Hoover Thermostat 16
1.2.2 Hamiltonian of the Material System 19
1.2.3 Objectivity in Molecular Dynamics 21
1.3 Thermoelasticity and Sequential Multiscale Modeling 24
1.3.1 Governing Equations of Thermoelasticity 24
1.3.2 Material Constants from Molecular Dynamics Simulation 26
1.3.2.1 Elastic Constants 27
1.3.2.2 Thermal Conductivity 29
1.3.2.3 Specific Heat and Thermal Expansion Coefficients 30
1.4 Concurrent Multiscale Modeling from Atoms to Genuine Continuum 30
1.4.1 One Specimen, Two Regions 30
1.4.2 Interfacial Conditions 33
1.4.3 Multiple Time Scale Algorithm 34
1.4.4 Sample Problems and Numerical Results 36
1.4.4.1 Material Constants Obtained from MD Simulations 37
1.4.4.2 Material Constants: Comparison with Other Researchers' Work 38
1.4.4.3 Case Studies 41
1.5 Discussions 47
References 49
2 Atomistic Modelling of Nanoindentation of Multilayered Graphene-Reinforced Nanocomposites 51
2.1 Introduction and Background 52
2.1.1 Experimental Techniques in Nanoindentation 53
2.1.2 Analytical Modelling of Nanoindentation 54
2.1.3 Atomistic Modelling of Nanoindentation 56
2.2 Basic Concepts of Molecular Dynamics Simulations 58
2.3 Molecular Dynamics Simulation of Graphene-Reinforced Nanocomposites 61
2.3.1 Indentation of a Single Layer of Graphene 62
2.3.2 Indentation of Multilayers of Graphene Sheets 65
2.3.3 Indentation of Polyethylene 67
2.3.4 Single-Layer Graphene-Reinforced Polyethylene 69
2.3.5 Graphene-Reinforced Multilayered Polyethylene Composites 72
2.4 Concluding Remarks 75
References 77
3 Molecular Dynamics Studies of Load Transfer in Nanocomposites Reinforced by Defective Carbon Nanotube 83
3.1 Introduction 84
3.1.1 Interfacial Shear Strength 84
3.1.2 Buckling Behavior 89
3.1.3 Objectives 91
3.2 Fundamental Aspects of MD Simulation Techniques 92
3.2.1 Numerical Simulation Techniques 92
3.2.2 Molecular Modeling of Pull-Out Simulation 94
3.2.2.1 Molecular Structure of CNTs with Defects and Functionalization 94
3.2.2.2 Cured versus Uncured Polymer 95
3.2.2.3 Construction of Nanocomposite RVE 96
3.2.3 Molecular Modeling of Compressive Load Simulation 97
3.2.3.1 Molecular Structure of CNTs with Defects 97
3.2.3.2 Construction of Freestanding CNT and Nanocomposite RVE 98
3.3 Molecular Dynamics Simulation 99
3.3.1 Pull-Out Simulation 99
3.3.1.1 CNT Pull-Out Method 99
3.3.1.2 Evaluation of ISS 100
3.3.2 Compressive Load Simulation 104
3.3.2.1 CNT and RVE Compressive Load Method 104
3.3.2.2 Evaluation of Buckling Behavior 104
3.4 Results and Discussions 107
3.4.1 Analysis of Pull-Out Simulation 107
3.4.1.1 MD Model Validation 107
3.4.1.2 Effect of Vacancy Defects upon ISS 110
3.4.1.3 Effect of Carbon Adatom upon ISS 114
3.4.1.4 Effect of SW Defect upon ISS 116
3.4.1.5 Effect of Phenyl Functional Group upon ISS 118
3.4.2 Analysis of Compressive Load Simulation 121
3.4.2.1 Effect of Vacancy Defect upon Freestanding SWCNTs 121
3.4.2.2 Effect of Missing Atoms upon Embedded SWCNTs 124
3.4.2.3 Effect of Vacancy Symmetry and Distribution upon Embedded SWCNTs 127
3.4.2.4 Effect of SW Defect upon Freestanding and Embedded SWCNTs 128
3.5 Conclusions 129
References 130
4 Electrical Conductivity of Carbon Nanotube- and Graphene-Based Nanocomposites 134
4.1 Introduction 134
4.2 The Theory 139
4.2.1 Effective-Medium Theory with a Perfect Interface 139
4.2.2 The Percolation Threshold 144
4.2.3 The Two-Scale Composite Model for Filler Agglomeration 145
4.2.4 The Interfacial Resistance 150
4.2.5 The Tunneling-Assisted Interfacial Conductivity 151
4.3 Results and Discussion 153
4.3.1 The Electrical Conductivity of CNT Nanocomposites 153
4.3.1.1 The Effective Electrical Conductivity of the Coated CNT 153
4.3.1.2 The Effective Electrical Conductivity of CNT Nanocomposites 154
4.3.1.3 The Effect of CNT Anisotropy 157
4.3.1.4 The Effective Electrical Conductivity with a Totally Insulating Matrix 157
4.3.2 The Electrical Conductivity of Agglomerated Graphene Nanocomposites 159
4.3.2.1 Homogeneously Dispersed Graphene Nanocomposites: Sample B 160
4.3.2.2 Agglomerated Graphene Nanocomposites: Sample A-HE, A-LC, and A 161
4.3.2.3 The Role of Agglomerate Shape on the Percolation Threshold 164
4.4 Conclusions 164
References 165
5 Mechanical Behavior of Nanowires with High-Order Surface Stress Effects 168
5.1 Introduction 168
5.2 Surface Stresses in Mathematical Descriptions 169
5.3 High-Order Surface Stresses in Two-Dimensional Configuration 172
5.3.1 Boundary Value Problem: A Circular Inclusion in an Infinite Matrix 174
5.4 High-Order Surface Stresses in Nanowires 176
5.4.1 Mechanical Behavior of NWs Based on Euler-Bernoulli Beam Theory 177
5.4.2 Mechanical Behavior of NWs Based on Timoshenko Beam Theory 178
5.5 Results and Discussion 179
5.5.1 The Stress Concentration Factor for a Circular Cavity in an Infinite Matrix 179
5.5.2 Mechanical Behavior of NWs 180
5.6 Conclusions 183
References 184
6 The Design of Nano-Inhomogeneities with Uniform Internal Strain in Anti-Plane Shear Deformations of Composite Solids 189
6.1 Introduction 190
6.2 Basic Equations 193
6.3 Single Inhomogeneity with Interface Effects that Achieves Uniform Internal Strain Induced by a Screw Dislocation 195
6.3.1 Analysis 195
6.3.2 Numerical Examples 199
6.4 Periodic Inhomogeneities with Interface Effects That Achieve Uniform Internal Strain Fields 202
6.4.1 Solution Procedure 203
6.4.2 Numerical Examples 207
6.5 Conclusions 211
References 212
7 Ballistic Performance of Bimodal Nanostructured and Nanotwin-Strengthened Metals 214
7.1 Introduction 215
7.2 Specimen Configuration and Idealized Microstructures 216
7.3 Constitutive Relations and Failure Criterion of the NG and NT Phases 217
7.3.1 Flow Stress and Johnson–Cook Plasticity Model and Failure Criterion of the NG Phase 219
7.3.2 Flow Stress and Johnson–Cook Plasticity Model and Failure Criterion of NT Phase 220
7.4 Results and Discussion 221
7.4.1 Ballistic Performance of the Bimodal NS Cu 221
7.4.1.1 Effects of Microstructure 221
7.4.1.2 Multiple Ballistic Indexes 223
7.4.2 Ballistic Performance of CG Metals Strengthened by NT Regions 225
7.4.2.1 Effects of Microstructure 225
7.4.2.2 Comparison with Single Phase CG Structure 229
7.5 Conclusions 230
References 231
8 Full-Field Micromechanics of Precipitated Shape Memory Alloys 234
8.1 Introduction 235
8.2 Modeling Approach 239
8.2.1 Computational Procedure 239
8.2.1.1 Microstructure Generation 239
8.2.1.2 Coherency Fields 240
8.2.1.3 Ni Concentration Fields 241
8.2.1.4 Simulations of the Effective Thermomechanical Response 241
8.2.2 Insight into the Computational Results 243
8.2.2.1 Coherency Stress, Ni concentration, and Mechanical Fields 244
8.2.2.2 Effective Thermomechanical Response 245
8.3 Prediction of the Effective Response of Precipitated NiTi 249
8.4 Discussion 255
Appendix: Constitutive Law for Polycrystalline SMAs 258
Variation of the Transformation Strain Magnitude 259
Description of a ``Smooth'' Thermomechanical Response 260
Calibration of the Model 260
References 261
9 Micromechanics of Ferroic Functional Materials 265
9.1 Introduction 265
9.2 Governing Equations, Constitutive Equations, and Material Description 267
9.3 Eshelby Tensor and Estimates of Composite Properties 270
9.4 Ferroic Crystal Variants and Domains 273
9.5 Laminates of Ferroic Crystal Variants 279
9.6 Applications in Polycrystalline Films 282
9.7 Conclusion 286
References 287
10 Micromechanics of Bone Modeled as a Composite Material 289
10.1 Introduction 289
10.1.1 Characteristics of Biological Materials 289
10.1.2 Hierarchical Composite Structure of Bone 290
10.1.3 Overview on Modeling of Bone 292
10.2 Elastic Hierarchical Modeling of Bone 293
10.2.1 Nanoscale 294
10.2.2 Sub-microscale 296
10.2.3 Microscale 300
10.2.4 Mesoscale Level 300
10.3 Trabecular Bone Anisotropy 303
10.4 Modeling of Plasticity, Damage, and Fracture of Bone 303
10.5 Apparent Properties 305
10.6 Bone as a Cosserat Material 307
10.7 Bone as a Viscoelastic Material 308
10.8 Conclusions 309
References 309
11 Linear Elastic Composites with Statistically Oriented Spheroidal Inclusions 315
11.1 Introduction 316
11.2 Theoretical Background 317
11.2.1 Affine Spaces, Open Subsets and Tangent Spaces 317
11.2.2 Tensors 319
11.2.3 Tensor Contractions and Tensor as Linear Maps 322
11.2.4 Metric Tensor and Scalar Products 323
11.2.5 Symmetries of Second- and Fourth-Order Tensors 324
11.2.6 Isotropic Second- and Fourth-Order Tensors 325
11.2.7 Transversely Isotropic Second- and Fourth-Order Tensors 327
11.2.8 Basic Relations of the Theory of Linear Elasticity 331
11.3 Composite Materials with Aligned Inclusions 334
11.3.1 Eshelby's Inclusion and Fourth-Order Tensor 334
11.3.2 Strain Concentration Tensor 336
11.3.3 Composites with Spheroidal Inclusions and the Aligned Case 338
11.4 Composite Materials with Statistically Oriented Inclusions 341
11.4.1 Generalised Walpole's Formula 341
11.4.2 Transversely Isotropic Case: Preliminaries 343
11.4.3 Transversely Isotropic Case: Average of a Function of the Direction 345
11.4.4 Transversely Isotropic Case: Solution in the Polar Parametrisation 347
11.4.5 Some Relevant Particular Cases 348
11.5 Discussion 350
In Memoriam 353
References 353
12 A Time-Incremental Eshelby-Based Homogenization Scheme for Viscoelastic Heterogeneous Materials 355
12.1 Introduction 355
12.2 Time-Incremental Formulation 358
12.2.1 Constitutive Equations 358
12.2.2 Time-Incremental Internal Variables Formulation 360
12.3 Viscoelastic Ellipsoidal Eshelby Inclusion 362
12.3.1 Strain Rate Concentration Equations 362
12.3.2 Interaction Laws 364
12.4 Homogenization and Results for Two-Phase Composite Materials 365
12.4.1 Homogenization for Two-Phase Composite Materials 365
12.4.2 Results and Discussion 366
12.4.2.1 Comparison with a Hereditary Approach 366
12.4.2.2 Comparison with Another Exact Internal Variable Approach 367
12.4.2.3 Comparisons with the ``Translated Fields'' Method and the ``Additive Law'' 371
12.5 Conclusions 373
References 375
13 Effects of Local Spin on Overall Properties of Granule Materials 378
13.1 Introduction 378
13.2 Literature Survey 380
13.3 Continuumnization for Rigid Body Grid 381
13.3.1 Motion and Force of Particle Assembly 381
13.3.2 Equation of Motion and Euler's Momentum Equation 383
13.3.3 Continuumnization of Translation and Spin 384
13.4 Nature of Material Properties for Continuumnized Functions 385
13.5 Vanishing of Spin 388
13.6 Characteristic Equation of Continuumnized Function 389
13.6.1 Characteristic Equation 391
13.6.2 Remaining of Local Torque in the Limit as a Goes to 0 394
13.7 Concluding Remarks 394
References 395
14 The Parametric HFGMC Micromechanics 397
14.1 Introduction 397
14.2 Nonlinear Doubly Periodic HFGMC Formulation: Regular Array 399
14.3 Nonlinear Doubly Periodic Parametric HFGMC Formulation 410
14.4 Nonlinear Triply Periodic Parametric HFGMC Formulation 415
14.5 HFGMC with Average Virtual Work Formulation 422
14.6 Applications 425
Appendix 427
References 429
15 On Parameterization of the Reinforcement Phase Distribution in Continuous Fiber-Reinforced Composites 431
15.1 Introduction 432
15.2 Experiments 433
15.2.1 Specimens and Experimental Tests 433
15.2.2 Microscopic Photographing and Image Processing 434
15.2.3 *-1pc 435
15.3 Statistical Analysis 436
15.3.1 Geometric Measures Influencing the Flexural Elastic Modulus Ef 436
15.3.2 Comparison of the Real Composite Cross-Sections and the Theoretical Models 439
15.4 Summary and Conclusions 440
References 441
16 Micromechanical Modeling of Polymeric Composite Materials with Moisture Absorption 443
16.1 Introduction 443
16.2 Micromechanical Framework 445
16.3 Modeling Moisture-Induced Damage in NFRCs(Pan and Zhong 2015) 450
16.3.1 Randomly Oriented Straight Inhomogeneity 451
16.3.2 Unidirectional Circular Cylindrical Inhomogeneity 455
16.4 Modeling Modulus Loss of the Wood Cell Wall(Pan and Zhong 2016) 459
16.4.1 Backgrounds 459
16.4.2 Unidirectional Circular Cylindrical Inhomogeneity 460
16.4.3 Results and Discussions 464
16.5 Conclusions 470
Appendix A 470
References 471
17 General Interface Integral Equations in Elasticity of Random Structure Composites 474
17.1 Introduction 474
17.2 Preliminaries 476
17.2.1 Basic Equations 476
17.2.2 Statistical Description of Random Structure Composites 478
17.2.3 Green's Function and Related Tensors 479
17.3 Effective Properties and Interface polarization Tensors 481
17.4 General Integral Equations 482
17.4.1 Perturbators for a Single Inclusion Inside a Macrodomain 482
17.4.2 General Integral Equation for a Microinhomogeneous Infinite Medium 487
17.4.3 Infinite Coupled System of General Integral Equations 490
17.5 Method of Fundamental Solutions (MFS) 491
17.5.1 The Scheme of the Method of Fundamental Solutions (MFS) 491
17.5.2 The Matrix Representation of the MFS 495
17.6 Some Classical Hypotheses and Approaches 497
17.7 Solution of GIEs 499
17.7.1 Classical Approaches with Volume Effective Fields 500
17.7.2 NBM's Method in Terms of the Volume Perturbator Factor 501
17.7.3 NBM's Method in Terms of the Interface Perturbator Factor 501
17.8 Numerical Results 503
17.9 Conclusion 507
References 508
Index 512