Multiscale Simulations and Mechanics of Biological Materials

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.

• About the Editors xvList of Contributors xviiPreface xxiPart I MULTISCALE SIMULATION THEORY1 Atomistic-to-Continuum Coupling Methods for Heat Transfer in Solids 3Gregory J. Wagner1.1 Introduction 31.2 The Coupled Temperature Field 51.2.1 Spatial Reduction 51.2.2 Time Averaging 61.3 Coupling the MD and Continuum Energy 71.3.1 The Coupled System 71.3.2 Continuum Heat Transfer 81.3.3 Augmented MD 81.4 Examples 91.4.1 One-Dimensional Heat Conduction 91.4.2 Thermal Response of a Composite System 101.5 Coupled Phonon-Electron Heat Transport 121.6 Examples: Phonon–Electron Coupling 141.6.1 Equilibration of Electron/Phonon Energies 141.6.2 Laser Heating of a Carbon Nanotube 151.7 Discussion 17Acknowledgments 18References 182 Accurate Boundary Treatments for Concurrent Multiscale Simulations 21Shaoqiang Tang2.1 Introduction 212.2 Time History Kernel Treatment 222.2.1 Harmonic Chain 222.2.2 Square Lattice 232.3 Velocity Interfacial Conditions: Matching the Differential Operator 272.4 MBCs: Matching the Dispersion Relation 302.4.1 Harmonic Chain 302.4.2 FCC Lattice 332.5 Accurate Boundary Conditions: Matching the Time History Kernel Function 362.6 Two-Way Boundary Conditions 392.7 Conclusions 41Acknowledgments 41References 413 A Multiscale Crystal Defect Dynamics and Its Applications 43Lisheng Liu and Shaofan Li3.1 Introduction 433.2 Multiscale Crystal Defect Dynamics 443.3 How and Why the MCDD Model Works 473.4 Multiscale Finite Element Discretization 473.5 Numerical Examples 523.6 Discussion 54Acknowledgments 54Appendix 55References 574 Application of Many-Realization Molecular Dynamics Method to Understand the Physics of Nonequilibrium Processes in Solids 59Yao Fu and Albert C. To4.1 Chapter Overview and Background 594.2 Many-Realization Method 604.3 Application of the Many-Realization Method to Shock Analysis 624.4 Conclusions 72Acknowledgments 74References 745 Multiscale, Multiphysics Modeling of Electromechanical Coupling in Surface-Dominated Nanostructures 77Harold S. Park and Michel Devel5.1 Introduction 775.2 Atomistic Electromechanical Potential Energy 795.2.1 Atomistic Electrostatic Potential Energy: Gaussian Dipole Method 805.2.2 Finite Element Equilibrium Equations from Total Electromechanical Potential Energy 835.3 Bulk Electrostatic Piola–Kirchoff Stress 845.3.1 Cauchy–Born Kinematics 845.3.2 Comparison of Bulk Electrostatic Stress with Molecular Dynamics Electrostatic Force 865.4 Surface Electrostatic Stress 875.5 One-Dimensional Numerical Examples 895.5.1 Verification of Bulk Electrostatic Stress 895.5.2 Verification of Surface Electrostatic Stress 915.6 Conclusions and Future Research 94Acknowledgments 95References 956 Towards a General Purpose Design System for Composites 99Jacob Fish6.1 Motivation 996.2 General Purpose Multiscale Formulation 1036.2.1 The Basic Reduced-Order Model 1036.2.2 Enhanced Reduced-Order Model 1046.3 Mechanistic Modeling of Fatigue via Multiple Temporal Scales 1066.4 Coupling of Mechanical and Environmental Degradation Processes 1076.4.1 Mathematical Model 1076.4.2 Mathematical Upscaling 1096.4.3 Computational Upscaling 1106.5 Uncertainty Quantification of Nonlinear Model of Micro-Interfaces and Micro-Phases 111References 113Part II PATIENT-SPECIFIC FLUID-STRUCTURE INTERACTION MODELING, SIMULATION AND DIAGNOSIS7 Patient-Specific Computational Fluid Mechanics of Cerebral Arteries with Aneurysm and Stent 119Kenji Takizawa, Kathleen Schjodt, Anthony Puntel, Nikolay Kostov, and Tayfun E. Tezduyar7.1 Introduction 1197.2 Mesh Generation 1207.3 Computational Results 1247.3.1 Computational Models 1247.3.2 Comparative Study 1317.3.3 Evaluation of Zero-Thickness Representation 1427.4 Concluding Remarks 145Acknowledgments 146References 1468 Application of Isogeometric Analysis to Simulate Local Nanoparticulate Drug Delivery in Patient-Specific Coronary Arteries 149Shaolie S. Hossain and Yongjie Zhang8.1 Introduction 1498.2 Materials and Methods 1518.2.1 Mathematical Modeling 1518.2.2 Parameter Selection 1568.2.3 Mesh Generation from Medical Imaging Data 1588.3 Results 1598.3.1 Extraction of NP Wall Deposition Data 1598.3.2 Drug Distribution in a Normal Artery Wall 1608.3.3 Drug Distribution in a Diseased Artery Wall with a Vulnerable Plaque 1608.4 Conclusions and Future Work 165Acknowledgments 166References 1669 Modeling and Rapid Simulation of High-Frequency Scattering Responses of Cellular Groups 169Tarek Ismail Zohdi9.1 Introduction 1699.2 Ray Theory: Scope of Use and General Remarks 1719.3 Ray Theory 1739.4 Plane Harmonic Electromagnetic Waves 1779.4.1 General Plane Waves 1779.4.2 Electromagnetic Waves 1779.4.3 Optical Energy Propagation 1789.4.4 Reflection and Absorption of Energy 1799.4.5 Computational Algorithm 1839.4.6 Thermal Conversion of Optical Losses 1879.5 Summary 190References 19010 Electrohydrodynamic Assembly of Nanoparticles for Nanoengineered Biosensors 193Jae-Hyun Chung, Hyun-Boo Lee, and Jong-Hoon Kim10.1 Introduction for Nanoengineered Biosensors 19310.2 Electric-Field-Induced Phenomena 19310.2.1 Electrophoresis 19410.2.2 Dielectrophoresis 19510.2.3 Electroosmotic and Electrothermal Flow 19810.2.4 Brownian Motion Forces and Drag Forces 19910.3 Geometry Dependency of Dielectrophoresis 20010.4 Electric-Field-Guided Assembly of Flexible Molecules in Combination with other Mechanisms 20310.4.1 Dielectrophoresis in Combination with Fluid Flow 20310.4.2 Dielectrophoresis in Combination with Binding Affinity 20310.4.3 Dielectrophoresis in Combination with Capillary Action and Viscosity 20310.5 Selective Assembly of Nanoparticles 20410.5.1 Size-Selective Deposition of Nanoparticles 20410.5.2 Electric-Property Sorting of Nanoparticles 20510.6 Summary and Applications 205References 20511 Advancements in the Immersed Finite-Element Method and Bio-Medical Applications 207Lucy Zhang, Xingshi Wang, and Chu Wang11.1 Introduction 20711.2 Formulation 20811.2.1 The Immersed Finite Element Method 20811.2.2 Semi-Implicit Immersed Finite Element Method 21011.3 Bio-Medical Applications 21111.3.1 Red Blood Cell in Bifurcated Vessels 21111.3.2 Human Vocal Folds Vibration during Phonation 21411.4 Conclusions 217References 21712 Immersed Methods for Compressible Fluid–Solid Interactions 219Xiaodong Sheldon Wang12.1 Background and Objectives 21912.2 Results and Challenges 22212.2.1 Formulations, Theories, and Results 22212.2.2 Stability Analysis 22712.2.3 Kernel Functions 22812.2.4 A Simple Model Problem 23112.2.5 Compressible Fluid Model for General Grids 23112.2.6 Multigrid Preconditioner 23212.3 Conclusion 234References 234Part III FROM CELLULAR STRUCTURE TO TISSUES AND ORGANS13 The Role of the Cortical Membrane in Cell Mechanics: Model and Simulation 241Louis Foucard, Xavier Espinet, Eduard Benet, and Franck J. Vernerey13.1 Introduction 24113.2 The Physics of the Membrane–Cortex Complex and Its Interactions 24313.2.1 The Mechanics of the Membrane–Cortex Complex 24313.2.2 Interaction of the Membrane with the Outer Environment 24713.3 Formulation of the Membrane Mechanics and Fluid–Membrane Interaction 24913.3.1 Kinematics of Immersed Membrane 24913.3.2 Variational Formulation of the Immersed MCC Problem 25113.3.3 Principle of Virtual Power and Conservation of Momentum 25313.4 The Extended Finite Element and the Grid-Based Particle Methods 25513.5 Examples 25713.5.1 The Equilibrium Shapes of the Red Blood Cell 25713.5.2 Cell Endocytosis 25913.5.3 Cell Blebbing 26013.6 Conclusion 262Acknowledgments 263References 26314 Role of Elastin in Arterial Mechanics 267Yanhang Zhang and Shahrokh Zeinali-Davarani14.1 Introduction 26714.2 The Role of Elastin in Vascular Diseases 26814.3 Mechanical Behavior of Elastin 26914.3.1 Orthotropic Hyperelasticity in Arterial Elastin 26914.3.2 Viscoelastic Behavior 27114.4 Constitutive Modeling of Elastin 27214.5 Conclusions 276Acknowledgments 276References 27715 Characterization of Mechanical Properties of Biological Tissue: Application to the FEM Analysis of the Urinary Bladder 283Eugenio Oñate, Facundo J. Bellomo, Virginia Monteiro, Sergio Oller, and Liz G. Nallim15.1 Introduction 28315.2 Inverse Approach for the Material Characterization of Biological Soft Tissues via a Generalized Rule of Mixtures 28415.2.1 Constitutive Model for Material Characterization 28415.2.2 Definition of the Objective Function and Materials Characterization Procedure 28615.2.3 Validation of the Inverse Model for Urinary Bladder Tissue Characterization 28715.3 FEM Analysis of the Urinary Bladder 28915.3.1 Constitutive Model for Tissue Analysis 29015.3.2 Validation. Test Inflation of a Quasi-incompressible Rubber Sphere 29215.3.3 Mechanical Simulation of Human Urinary Bladder 29315.3.4 Study of Urine–Bladder Interaction 29515.4 Conclusions 298Acknowledgments 298References 29816 Structure Design of Vascular Stents 301Yaling Liu, Jie Yang, Yihua Zhou, and Jia Hu16.1 Introduction 30116.2 Ideal Vascular Stents 30316.3 Design Parameters that Affect the Properties of Stents 30416.3.1 Expansion Method 30516.3.2 Stent Materials 30516.3.3 Structure of Stents 30616.3.4 Effect of Design Parameters on Stent Properties 30816.4 Main Methods for Vascular Stent Design 30816.5 Vascular Stent Design Method Perspective 316References 31617 Applications of Meshfree Methods in Explicit Fracture and Medical Modeling 319Daniel C. Simkins, Jr.17.1 Introduction 31917.2 Explicit Crack Representation 31917.2.1 Two-Dimensional Cracks 32017.2.2 Three-Dimensional Cracks in Thin Shells 32317.2.3 Material Model Requirements 32317.2.4 Crack Examples 32317.3 Meshfree Modeling in Medicine 327Acknowledgments 331References 33118 Design of Dynamic and Fatigue-Strength-Enhanced Orthopedic Implants 333Sagar Bhamare, Seetha Ramaiah Mannava, Leonora Felon, David Kirschman, Vijay Vasudevan, and Dong Qian18.1 Introduction 33318.2 Fatigue Life Analysis of Orthopedic Implants 33518.2.1 Fatigue Life Testing for Implants 33518.2.2 Fatigue Life Prediction 33718.3 LSP Process 33818.4 LSP Modeling and Simulation 33918.4.1 Pressure Pulse Model 33918.4.2 Constitutive Model 34018.4.3 Solution Procedure 34118.5 Application Example 34218.5.1 Implant Rod Design 34218.5.2 Residual Stresses 34218.5.3 Fatigue Tests and Life Predictions 34418.6 Summary 348Acknowledgments 348References 349Part IV BIO-MECHANICS AND MATERIALS OF BONES AND COLLAGENS19 Archetype Blending Continuum Theory and Compact Bone Mechanics 353Khalil I. Elkhodary, Michael Steven Greene, and Devin O’Connor19.1 Introduction 35319.1.1 A Short Look at the Hierarchical Structure of Bone 35419.1.2 A Background of Generalized Continuum Mechanics 35519.1.3 Notes on the Archetype Blending Continuum Theory 35619.2 ABC Formulation 35819.2.1 Physical Postulates and the Resulting Kinematics 35819.2.2 ABC Variational Formulation 35919.3 Constitutive Modeling in ABC 36119.3.1 General Concept 36119.3.2 Blending Laws for Cortical Bone Modeling 36319.4 The ABC Computational Model 36719.5 Results and Discussion 36819.5.1 Propagating Strain Inhomogeneities across Osteons 36819.5.2 Normal and Shear Stresses in Osteons 36919.5.3 Rotation and Displacement Fields in Osteons 37019.5.4 Damping in Cement Lines 37219.5.5 Qualitative Look at Strain Gradients in Osteons 37219.6 Conclusion 373Acknowledgments 374References 37420 Image-Based Multiscale Modeling of Porous Bone Materials 377Judy P. Yang, Sheng-Wei Chi, and Jiun-Shyan Chen20.1 Overview 37720.2 Homogenization of Porous Microstructures 37920.2.1 Basic Equations of Two-Phase Media 37920.2.2 Asymptotic Expansion of Two-Phase Medium 38120.2.3 Homogenized Porous Media 38620.3 Level Set Method for Image Segmentation 38720.3.1 Variational Level Set Formulation 38720.3.2 Strong Form Collocation Methods for Active Contour Model 38920.4 Image-Based Microscopic Cell Modeling 39120.4.1 Solution of Microscopic Cell Problems 39120.4.2 Reproducing Kernel and Gradient-Reproducing Kernel Approximations 39220.4.3 Gradient-Reproducing Kernel Collocation Method 39320.5 Trabecular Bone Modeling 39520.6 Conclusions 399Acknowledgment 399References 39921 Modeling Nonlinear Plasticity of Bone Mineral from Nanoindentation Data 403Amir Reza Zamiri and Suvranu De21.1 Introduction 40321.2 Methods 40421.3 Results 40721.4 Conclusions 408Acknowledgments 408References 40822 Mechanics of Cellular Materials and its Applications 411Ji Hoon Kim, Daeyong Kim, and Myoung-Gyu Lee22.1 Biological Cellular Materials 41122.1.1 Structure of Bone 41122.1.2 Mechanical Properties of Bone 41122.1.3 Failure of Bone 41522.1.4 Simulation of Bone 41722.2 Engineered Cellular Materials 42122.2.1 Constitutive Models for Metal Foams 42222.2.2 Structure Modeling of Cellular Materials 42422.2.3 Simulation of Cellular Materials 428References 43123 Biomechanics of Mineralized Collagens 435Ashfaq Adnan, Farzad Sarker, and Sheikh F. Ferdous23.1 Introduction 43523.1.1 Mineralized Collagen 43523.1.2 Molecular Origin and Structure of Mineralized Collagen 43623.1.3 Bone Remodeling, Bone Marrow Microenvironment, and Biomechanics of Mineralized Collagen 43823.2 Computational Method 43823.2.1 Molecular Structure of Mineralized Collagen 43823.2.2 The Constant-pH Molecular Dynamics Simulation 44123.3 Results 44123.3.1 First-Order Estimation of pH-Dependent TC–HAP Interaction Possibility 44123.3.2 pH-Dependent TC–HAP Interface Interactions 44323.4 Summary and Conclusions 446Acknowledgments 446References 446Index 449