Multiscale Simulations and Mechanics of Biological Materials
A compilation of recent developments in multiscale simulation and computational biomaterials written by leading specialists in the field
Presenting the latest developments in multiscale mechanics and multiscale simulations, and offering a unique viewpoint on multiscale modelling of biological materials, this book outlines the latest developments in computational biological materials from atomistic and molecular scale simulation on DNA, proteins, and nano-particles, to meoscale soft matter modelling of cells, and to macroscale soft tissue and blood vessel, and bone simulations. Traditionally, computational biomaterials researchers come from biological chemistry and biomedical engineering, so this is probably the first edited book to present work from these talented computational mechanics researchers.
The book has been written to honor Professor Wing Liu of Northwestern University, USA, who has made pioneering contributions in multiscale simulation and computational biomaterial in specific simulation of drag delivery at atomistic and molecular scale and computational cardiovascular fluid mechanics via immersed finite element method.
Key features:
- Offers a unique interdisciplinary approach to multiscale biomaterial modelling aimed at both accessible introductory and advanced levels
- Presents a breadth of computational approaches for modelling biological materials across multiple length scales (molecular to whole-tissue scale), including solid and fluid based approaches
- A companion website for supplementary materials plus links to contributors’ websites (www.wiley.com/go/li/multiscale)
Table of Contents:
About the Editors xv
List of Contributors xvii
Preface xxi
Part I MULTISCALE SIMULATION THEORY
1 Atomistic-to-Continuum Coupling Methods for Heat Transfer in Solids 3
Gregory J. Wagner
1.1 Introduction 3
1.2 The Coupled Temperature Field 5
1.2.1 Spatial Reduction 5
1.2.2 Time Averaging 6
1.3 Coupling the MD and Continuum Energy 7
1.3.1 The Coupled System 7
1.3.2 Continuum Heat Transfer 8
1.3.3 Augmented MD 8
1.4 Examples 9
1.4.1 One-Dimensional Heat Conduction 9
1.4.2 Thermal Response of a Composite System 10
1.5 Coupled Phonon-Electron Heat Transport 12
1.6 Examples: Phonon–Electron Coupling 14
1.6.1 Equilibration of Electron/Phonon Energies 14
1.6.2 Laser Heating of a Carbon Nanotube 15
1.7 Discussion 17
Acknowledgments 18
References 18
2 Accurate Boundary Treatments for Concurrent Multiscale Simulations 21
Shaoqiang Tang
2.1 Introduction 21
2.2 Time History Kernel Treatment 22
2.2.1 Harmonic Chain 22
2.2.2 Square Lattice 23
2.3 Velocity Interfacial Conditions: Matching the Differential Operator 27
2.4 MBCs: Matching the Dispersion Relation 30
2.4.1 Harmonic Chain 30
2.4.2 FCC Lattice 33
2.5 Accurate Boundary Conditions: Matching the Time History Kernel Function 36
2.6 Two-Way Boundary Conditions 39
2.7 Conclusions 41
Acknowledgments 41
References 41
3 A Multiscale Crystal Defect Dynamics and Its Applications 43
Lisheng Liu and Shaofan Li
3.1 Introduction 43
3.2 Multiscale Crystal Defect Dynamics 44
3.3 How and Why the MCDD Model Works 47
3.4 Multiscale Finite Element Discretization 47
3.5 Numerical Examples 52
3.6 Discussion 54
Acknowledgments 54
Appendix 55
References 57
4 Application of Many-Realization Molecular Dynamics Method to Understand the Physics of Nonequilibrium Processes in Solids 59
Yao Fu and Albert C. To
4.1 Chapter Overview and Background 59
4.2 Many-Realization Method 60
4.3 Application of the Many-Realization Method to Shock Analysis 62
4.4 Conclusions 72
Acknowledgments 74
References 74
5 Multiscale, Multiphysics Modeling of Electromechanical Coupling in Surface-Dominated Nanostructures 77
Harold S. Park and Michel Devel
5.1 Introduction 77
5.2 Atomistic Electromechanical Potential Energy 79
5.2.1 Atomistic Electrostatic Potential Energy: Gaussian Dipole Method 80
5.2.2 Finite Element Equilibrium Equations from Total Electromechanical Potential Energy 83
5.3 Bulk Electrostatic Piola–Kirchoff Stress 84
5.3.1 Cauchy–Born Kinematics 84
5.3.2 Comparison of Bulk Electrostatic Stress with Molecular Dynamics Electrostatic Force 86
5.4 Surface Electrostatic Stress 87
5.5 One-Dimensional Numerical Examples 89
5.5.1 Verification of Bulk Electrostatic Stress 89
5.5.2 Verification of Surface Electrostatic Stress 91
5.6 Conclusions and Future Research 94
Acknowledgments 95
References 95
6 Towards a General Purpose Design System for Composites 99
Jacob Fish
6.1 Motivation 99
6.2 General Purpose Multiscale Formulation 103
6.2.1 The Basic Reduced-Order Model 103
6.2.2 Enhanced Reduced-Order Model 104
6.3 Mechanistic Modeling of Fatigue via Multiple Temporal Scales 106
6.4 Coupling of Mechanical and Environmental Degradation Processes 107
6.4.1 Mathematical Model 107
6.4.2 Mathematical Upscaling 109
6.4.3 Computational Upscaling 110
6.5 Uncertainty Quantification of Nonlinear Model of Micro-Interfaces and Micro-Phases 111
References 113
Part II PATIENT-SPECIFIC FLUID-STRUCTURE INTERACTION MODELING, SIMULATION AND DIAGNOSIS
7 Patient-Specific Computational Fluid Mechanics of Cerebral Arteries with Aneurysm and Stent 119
Kenji Takizawa, Kathleen Schjodt, Anthony Puntel, Nikolay Kostov, and Tayfun E. Tezduyar
7.1 Introduction 119
7.2 Mesh Generation 120
7.3 Computational Results 124
7.3.1 Computational Models 124
7.3.2 Comparative Study 131
7.3.3 Evaluation of Zero-Thickness Representation 142
7.4 Concluding Remarks 145
Acknowledgments 146
References 146
8 Application of Isogeometric Analysis to Simulate Local Nanoparticulate Drug Delivery in Patient-Specific Coronary Arteries 149
Shaolie S. Hossain and Yongjie Zhang
8.1 Introduction 149
8.2 Materials and Methods 151
8.2.1 Mathematical Modeling 151
8.2.2 Parameter Selection 156
8.2.3 Mesh Generation from Medical Imaging Data 158
8.3 Results 159
8.3.1 Extraction of NP Wall Deposition Data 159
8.3.2 Drug Distribution in a Normal Artery Wall 160
8.3.3 Drug Distribution in a Diseased Artery Wall with a Vulnerable Plaque 160
8.4 Conclusions and Future Work 165
Acknowledgments 166
References 166
9 Modeling and Rapid Simulation of High-Frequency Scattering Responses of Cellular Groups 169
Tarek Ismail Zohdi
9.1 Introduction 169
9.2 Ray Theory: Scope of Use and General Remarks 171
9.3 Ray Theory 173
9.4 Plane Harmonic Electromagnetic Waves 177
9.4.1 General Plane Waves 177
9.4.2 Electromagnetic Waves 177
9.4.3 Optical Energy Propagation 178
9.4.4 Reflection and Absorption of Energy 179
9.4.5 Computational Algorithm 183
9.4.6 Thermal Conversion of Optical Losses 187
9.5 Summary 190
References 190
10 Electrohydrodynamic Assembly of Nanoparticles for Nanoengineered Biosensors 193
Jae-Hyun Chung, Hyun-Boo Lee, and Jong-Hoon Kim
10.1 Introduction for Nanoengineered Biosensors 193
10.2 Electric-Field-Induced Phenomena 193
10.2.1 Electrophoresis 194
10.2.2 Dielectrophoresis 195
10.2.3 Electroosmotic and Electrothermal Flow 198
10.2.4 Brownian Motion Forces and Drag Forces 199
10.3 Geometry Dependency of Dielectrophoresis 200
10.4 Electric-Field-Guided Assembly of Flexible Molecules in Combination with other Mechanisms 203
10.4.1 Dielectrophoresis in Combination with Fluid Flow 203
10.4.2 Dielectrophoresis in Combination with Binding Affinity 203
10.4.3 Dielectrophoresis in Combination with Capillary Action and Viscosity 203
10.5 Selective Assembly of Nanoparticles 204
10.5.1 Size-Selective Deposition of Nanoparticles 204
10.5.2 Electric-Property Sorting of Nanoparticles 205
10.6 Summary and Applications 205
References 205
11 Advancements in the Immersed Finite-Element Method and Bio-Medical Applications 207
Lucy Zhang, Xingshi Wang, and Chu Wang
11.1 Introduction 207
11.2 Formulation 208
11.2.1 The Immersed Finite Element Method 208
11.2.2 Semi-Implicit Immersed Finite Element Method 210
11.3 Bio-Medical Applications 211
11.3.1 Red Blood Cell in Bifurcated Vessels 211
11.3.2 Human Vocal Folds Vibration during Phonation 214
11.4 Conclusions 217
References 217
12 Immersed Methods for Compressible Fluid–Solid Interactions 219
Xiaodong Sheldon Wang
12.1 Background and Objectives 219
12.2 Results and Challenges 222
12.2.1 Formulations, Theories, and Results 222
12.2.2 Stability Analysis 227
12.2.3 Kernel Functions 228
12.2.4 A Simple Model Problem 231
12.2.5 Compressible Fluid Model for General Grids 231
12.2.6 Multigrid Preconditioner 232
12.3 Conclusion 234
References 234
Part III FROM CELLULAR STRUCTURE TO TISSUES AND ORGANS
13 The Role of the Cortical Membrane in Cell Mechanics: Model and Simulation 241
Louis Foucard, Xavier Espinet, Eduard Benet, and Franck J. Vernerey
13.1 Introduction 241
13.2 The Physics of the Membrane–Cortex Complex and Its Interactions 243
13.2.1 The Mechanics of the Membrane–Cortex Complex 243
13.2.2 Interaction of the Membrane with the Outer Environment 247
13.3 Formulation of the Membrane Mechanics and Fluid–Membrane Interaction 249
13.3.1 Kinematics of Immersed Membrane 249
13.3.2 Variational Formulation of the Immersed MCC Problem 251
13.3.3 Principle of Virtual Power and Conservation of Momentum 253
13.4 The Extended Finite Element and the Grid-Based Particle Methods 255
13.5 Examples 257
13.5.1 The Equilibrium Shapes of the Red Blood Cell 257
13.5.2 Cell Endocytosis 259
13.5.3 Cell Blebbing 260
13.6 Conclusion 262
Acknowledgments 263
References 263
14 Role of Elastin in Arterial Mechanics 267
Yanhang Zhang and Shahrokh Zeinali-Davarani
14.1 Introduction 267
14.2 The Role of Elastin in Vascular Diseases 268
14.3 Mechanical Behavior of Elastin 269
14.3.1 Orthotropic Hyperelasticity in Arterial Elastin 269
14.3.2 Viscoelastic Behavior 271
14.4 Constitutive Modeling of Elastin 272
14.5 Conclusions 276
Acknowledgments 276
References 277
15 Characterization of Mechanical Properties of Biological Tissue: Application to the FEM Analysis of the Urinary Bladder 283
Eugenio Oñate, Facundo J. Bellomo, Virginia Monteiro, Sergio Oller, and Liz G. Nallim
15.1 Introduction 283
15.2 Inverse Approach for the Material Characterization of Biological Soft Tissues via a Generalized Rule of Mixtures 284
15.2.1 Constitutive Model for Material Characterization 284
15.2.2 Definition of the Objective Function and Materials Characterization Procedure 286
15.2.3 Validation of the Inverse Model for Urinary Bladder Tissue Characterization 287
15.3 FEM Analysis of the Urinary Bladder 289
15.3.1 Constitutive Model for Tissue Analysis 290
15.3.2 Validation. Test Inflation of a Quasi-incompressible Rubber Sphere 292
15.3.3 Mechanical Simulation of Human Urinary Bladder 293
15.3.4 Study of Urine–Bladder Interaction 295
15.4 Conclusions 298
Acknowledgments 298
References 298
16 Structure Design of Vascular Stents 301
Yaling Liu, Jie Yang, Yihua Zhou, and Jia Hu
16.1 Introduction 301
16.2 Ideal Vascular Stents 303
16.3 Design Parameters that Affect the Properties of Stents 304
16.3.1 Expansion Method 305
16.3.2 Stent Materials 305
16.3.3 Structure of Stents 306
16.3.4 Effect of Design Parameters on Stent Properties 308
16.4 Main Methods for Vascular Stent Design 308
16.5 Vascular Stent Design Method Perspective 316
References 316
17 Applications of Meshfree Methods in Explicit Fracture and Medical Modeling 319
Daniel C. Simkins, Jr.
17.1 Introduction 319
17.2 Explicit Crack Representation 319
17.2.1 Two-Dimensional Cracks 320
17.2.2 Three-Dimensional Cracks in Thin Shells 323
17.2.3 Material Model Requirements 323
17.2.4 Crack Examples 323
17.3 Meshfree Modeling in Medicine 327
Acknowledgments 331
References 331
18 Design of Dynamic and Fatigue-Strength-Enhanced Orthopedic Implants 333
Sagar Bhamare, Seetha Ramaiah Mannava, Leonora Felon, David Kirschman, Vijay Vasudevan, and Dong Qian
18.1 Introduction 333
18.2 Fatigue Life Analysis of Orthopedic Implants 335
18.2.1 Fatigue Life Testing for Implants 335
18.2.2 Fatigue Life Prediction 337
18.3 LSP Process 338
18.4 LSP Modeling and Simulation 339
18.4.1 Pressure Pulse Model 339
18.4.2 Constitutive Model 340
18.4.3 Solution Procedure 341
18.5 Application Example 342
18.5.1 Implant Rod Design 342
18.5.2 Residual Stresses 342
18.5.3 Fatigue Tests and Life Predictions 344
18.6 Summary 348
Acknowledgments 348
References 349
Part IV BIO-MECHANICS AND MATERIALS OF BONES AND COLLAGENS
19 Archetype Blending Continuum Theory and Compact Bone Mechanics 353
Khalil I. Elkhodary, Michael Steven Greene, and Devin O’Connor
19.1 Introduction 353
19.1.1 A Short Look at the Hierarchical Structure of Bone 354
19.1.2 A Background of Generalized Continuum Mechanics 355
19.1.3 Notes on the Archetype Blending Continuum Theory 356
19.2 ABC Formulation 358
19.2.1 Physical Postulates and the Resulting Kinematics 358
19.2.2 ABC Variational Formulation 359
19.3 Constitutive Modeling in ABC 361
19.3.1 General Concept 361
19.3.2 Blending Laws for Cortical Bone Modeling 363
19.4 The ABC Computational Model 367
19.5 Results and Discussion 368
19.5.1 Propagating Strain Inhomogeneities across Osteons 368
19.5.2 Normal and Shear Stresses in Osteons 369
19.5.3 Rotation and Displacement Fields in Osteons 370
19.5.4 Damping in Cement Lines 372
19.5.5 Qualitative Look at Strain Gradients in Osteons 372
19.6 Conclusion 373
Acknowledgments 374
References 374
20 Image-Based Multiscale Modeling of Porous Bone Materials 377
Judy P. Yang, Sheng-Wei Chi, and Jiun-Shyan Chen
20.1 Overview 377
20.2 Homogenization of Porous Microstructures 379
20.2.1 Basic Equations of Two-Phase Media 379
20.2.2 Asymptotic Expansion of Two-Phase Medium 381
20.2.3 Homogenized Porous Media 386
20.3 Level Set Method for Image Segmentation 387
20.3.1 Variational Level Set Formulation 387
20.3.2 Strong Form Collocation Methods for Active Contour Model 389
20.4 Image-Based Microscopic Cell Modeling 391
20.4.1 Solution of Microscopic Cell Problems 391
20.4.2 Reproducing Kernel and Gradient-Reproducing Kernel Approximations 392
20.4.3 Gradient-Reproducing Kernel Collocation Method 393
20.5 Trabecular Bone Modeling 395
20.6 Conclusions 399
Acknowledgment 399
References 399
21 Modeling Nonlinear Plasticity of Bone Mineral from Nanoindentation Data 403
Amir Reza Zamiri and Suvranu De
21.1 Introduction 403
21.2 Methods 404
21.3 Results 407
21.4 Conclusions 408
Acknowledgments 408
References 408
22 Mechanics of Cellular Materials and its Applications 411
Ji Hoon Kim, Daeyong Kim, and Myoung-Gyu Lee
22.1 Biological Cellular Materials 411
22.1.1 Structure of Bone 411
22.1.2 Mechanical Properties of Bone 411
22.1.3 Failure of Bone 415
22.1.4 Simulation of Bone 417
22.2 Engineered Cellular Materials 421
22.2.1 Constitutive Models for Metal Foams 422
22.2.2 Structure Modeling of Cellular Materials 424
22.2.3 Simulation of Cellular Materials 428
References 431
23 Biomechanics of Mineralized Collagens 435
Ashfaq Adnan, Farzad Sarker, and Sheikh F. Ferdous
23.1 Introduction 435
23.1.1 Mineralized Collagen 435
23.1.2 Molecular Origin and Structure of Mineralized Collagen 436
23.1.3 Bone Remodeling, Bone Marrow Microenvironment, and Biomechanics of Mineralized Collagen 438
23.2 Computational Method 438
23.2.1 Molecular Structure of Mineralized Collagen 438
23.2.2 The Constant-pH Molecular Dynamics Simulation 441
23.3 Results 441
23.3.1 First-Order Estimation of pH-Dependent TC–HAP Interaction Possibility 441
23.3.2 pH-Dependent TC–HAP Interface Interactions 443
23.4 Summary and Conclusions 446
Acknowledgments 446
References 446
Index 449
About the Author :
Shaofan Li is Professor of Applied and Computational Mechanics in the Department of Civil and Environmental Engineering at University of California, Berkeley, USA. He gained his PhD in Mechanical Engineering from Northwestern University, Illinois, in 1997, having previously earned his MSc in Aerospace Engineering. His current research interests include Meshfree Simulations of Adiabatic Shear Band and Spall Fracture, Simulations of Stem Cell Differentiations, and Multiscale Non-equilibrium Equilibrium Molecular Dynamics. Dr Li is the author of numerous articles and conference proceedings.
Dong Qian is Associate Professor of Mechanical Engineering and Director of Graduate Study for the Mechanical Engineering Program at the University of Cincinnati, USA. He obtained his BS degree in Bridge Engineering in 1994 from Tongji University in China. He came to US in 1996 and obtained M.S. degree in civil engineering at the University of Missouri-Columbia in 1998. Dr. Qian is a member of the US association for computational mechanics and ASME. He has published over 40 journal papers and book chapters. His research interests include nano-scale modeling, simulation and applications, meshfree methods, and development of multi-scale methods in solid mechanics.
