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
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.
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.