Multiscale Simulations and Mechanics of Biological Materials

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 Onate, 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