Multiscale Biomechanics: Theory and Applications

ISBN-13: 9781119033691 / Angielski / Twarda / 2023 / 624 str.

S Mohammadi

Spis treści

ContentsPreface xiiiList of Abbreviations xviiPart I Introduction 11 Introduction 31.1 Introduction to Biomechanics 31.2 Biology and Biomechanics 31.3 Types of Biological Systems 61.3.1 Biosolids 61.3.2 Biofluids 71.3.3 Biomolecules 81.3.4 Synthesized Biosystems 91.4 Biomechanical Hierarchy 101.4.1 Organ Level 101.4.2 Tissue Level 111.4.3 Cellular and Lower Levels 121.4.4 Complex Medical Procedures 131.5 Multiscale/Multiphysics Analysis 131.6 Scope of the Book 17Part II Analytical and Numerical Bases 212 Theoretical Bases of Continuum Mechanics 232.1 Introduction 232.2 Solid Mechanics 232.2.1 Elasticity 242.2.2 Plasticity 282.2.3 Damage Mechanics 312.2.4 Fracture Mechanics 362.2.5 Viscoelasticity 532.2.6 Poroelasticity 592.2.7 Large Deformation 632.3 Flow, Convection and Diffusion 722.3.1 Thermodynamics 722.3.2 Fluid Mechanics 742.3.3 Gas Dynamics 782.3.4 Diffusion and Convection 812.4 Fluid-Structure Interaction 832.4.1 Lagrangian and Eulerian Descriptions 832.4.2 Fluid-Solid Interface Boundary Conditions 842.4.3 Governing Equations in the Eulerian Description 852.4.4 Coupled Lagrangian-Eulerian (CLE) 862.4.5 Coupled Lagrangian-Lagrangian (CLL) 872.4.6 Arbitrary Lagrangian-Eulerian (ALE) 883 Numerical Methods 933.1 Introduction 933.2 Finite Difference Method (FDM) 933.2.1 One-Dimensional FDM 943.2.2 Higher Order One-Dimensional FDM 953.2.3 FDM for Solving Partial Differential Equations 983.3 Finite Volume Method (FVM) 993.4 Finite Element Method (FEM) 1023.4.1 Basics of FEM Interpolation 1023.4.2 FEM Basis Functions/Shape Functions 1033.4.3 Properties of the Finite Element Interpolation 1053.4.4 Physical and Parametric Coordinate Systems 1063.4.5 Main Types of Finite Elements 1063.4.6 Governing Equations of the Boundary Value Problem 1093.4.7 Numerical Integration 1123.5 Extended Finite Element Method (XFEM) 1133.5.1 A Review of XFEM Development 1133.5.2 Partition of Unity 1143.5.3 Enrichments 1153.5.4 Signed Distance Function 1153.5.5 XFEM Approximation for Cracked Elements 1153.5.6 Boundary Value Problem for a Cracked Body 1173.5.7 XFEM Discretisation of the Governing Equation 1183.5.8 Numerical Integration 1193.5.9 Selection of Enrichment Nodes for Crack Propagation 1213.5.10 Incompatible Modes of XFEM Enrichments 1223.5.11 The Level Set Method for Tracking Moving Boundaries 1233.5.12 XFEM Tip Enrichments 1243.5.13 XFEM Enrichment Formulation for Large Deformation Problems 1323.6 Extended Isogeometric Analysis (XIGA) 1333.6.1 Introduction 1333.6.2 Isogeometric Analysis 1333.6.3 Extended Isogeometric Analysis (XIGA) 1363.6.4 XIGA Governing Equations 1383.6.5 Numerical Integration 1403.7 Meshless Methods 1423.7.1 Why Going Meshless 1423.7.2 Meshless Approximations 1433.7.3 Meshless Solutions for the Boundary Value Problems 1583.8 Variable Node Element (VNE) 1664 Multiscale Methods 1714.1 Introduction 1714.2 Homogenization Methods 1724.2.1 Introduction 1724.2.2 Representative Volume Element (RVE) 1734.2.3 Mathematical Homogenization 1744.2.4 Computational Homogenization 1814.3 Molecular Dynamics (MD) 1954.3.1 Introduction 1954.3.2 Statistical Mechanics 1964.3.3 MD Equations of Motion 2114.3.4 Models for Atomic Interactions - MD Potentials 2154.3.5 Measures for Determining the State of MD Systems 2224.3.6 Stress Computation in MD 2234.3.7 Molecular Statics 2264.3.8 Sample MD Simulation of a Polymer 2274.4 Sequential Multiscale Method 2294.4.1 Introduction 2294.4.2 Multiscale Modelling of CNT Reinforced Concrete 2304.4.3 Molecular Dynamics Simulation of CNTs 2314.4.4 Simulation of CNT-Reinforced Calcium Silicate Hydrate 2424.4.5 Micromechanical Simulation of CNT-Reinforced Cement 2474.4.6 Mesoscale Simulation of CNT-Reinforced Concrete 2504.4.7 Macroscale Simulation of CNT-Reinforced Concrete 2564.5 Concurrent Multiscale Methods 2584.5.1 Introduction 2584.5.2 Quasi-Continuum Method (QC) 2604.5.3 Bridging Domain Method (BDM) 2674.5.4 Bridging Scale Method (BSM) 2714.5.5 Disordered Concurrent Multiscale Method (DCMM) 2724.5.6 Variable Node Multiscale Method (VNMM) 2814.5.7 Enriched Multiscale Method (EMM) 288Part III Biomechanical Simulations 2975 Biomechanics of Soft Tissues 2995.1 Introduction 2995.2 Physiology of Soft Tissues 3005.2.1 Soft Tissues, Skin 3005.2.2 Artery 3035.2.3 Heart Leaflet 3035.2.4 Brain Tissue 3045.3 Hyperelastic Models of Soft Tissues 3055.3.1 Introduction 3055.3.2 Description of Deformation and Definition of Invariants 3075.3.3 Isotropic neo-Hookean Hyperelastic Model 3095.3.4 Isotropic Mooney-Rivlin Hyperelastic Model 3125.3.5 Hyperelastic Models for Multiscale Simulation of Tendon 3135.3.6 Anisotropic Hyperelastic Models for Fibrous Tissues 3165.3.7 Polyconvex Undamaged Functions for Fibrous Tissues 3195.3.8 Damaged Soft Tissue 3215.4 Multiscale Modelling of Undamaged Tendon 3285.4.1 Fibril Scale 3305.4.2 Fibre Scale 3305.4.3 Tissue Scale 3325.5 Multiscale Analysis of a Human Aortic Heart Valve 3365.5.1 Introduction 3365.5.2 Organ Scale Simulation 3375.5.3 Simulation in the Tissue Scale 3425.5.4 Cell Scale Analysis 3475.6 Modelling of Ligament Damage 3495.7 Modelling of the Peeling Test: Dissection of the Medial Tissue 3555.8 Healing in Damaged Soft Tissue 3595.8.1 Introduction 3595.8.2 Physical Foundation of Tissue Healing 3605.8.3 Solution Procedure 3695.8.4 Numerical Analysis 3725.9 Hierarchical Multiscale Modelling of a Degraded Arterial Wall 3835.9.1 Definition of the Problem 3835.9.2 Multiscale Model 3875.9.3 Hyperelastic Material Models 3895.9.4 Computational Framework of the Hierarchical Multiscale Homogenization 3905.9.5 Numerical Results 3945.10 Multiscale Modelling of the Brain 4015.10.1 Introduction 4015.10.2 Biomechanics of the Brain 4025.10.3 Multiscale Modelling of the Brain (neo-Hookean Model) 4035.10.4 Viscoelastic Modelling of the Brain 4146 Biomechanics of Hard Tissues 4236.1 Introduction 4236.1.1 Hard Tissues 4236.1.2 Chemical Composition of Bone 4236.1.3 Multiscale Structure of Bone 4236.1.4 Bone Remodelling 4286.1.5 Contents of the Chapter 4296.2 Concepts of Fracture Analysis of Hard Tissues 4296.2.1 Numerical Studies of Bone Fracture 4306.2.2 Constitutive Response of the Bone 4336.2.3 Poroelastic Nature of Bone Tissues 4336.2.4 Plasticity and Damage 4336.2.5 Hyperelastic Response 4356.3 Simulation of the Femur Bone at Multiple Scales 4356.3.1 Microscale Simulation of the Trabecular Bone 4366.3.2 Two-dimensional XFEM Mesoscale Fracture Simulation of the Cortical Bone 4376.3.3 Macroscale Simulation of the Femur 4436.4 Healing in Damaged Hard Tissue 4466.4.1 Introduction 4466.4.2 Physical Foundation of Bone Tissue Healing 4486.4.3 Solution Procedure 4556.4.4 Numerical Analysis 4587 Supplementary Topics 4677.1 Introduction 4677.2 Shape Memory Alloy (SMA) Stenting of an Artery 4687.2.1 Stenting Procedures 4687.2.2 SMA Constitutive Equations 4697.2.3 Contact Mechanics 4717.2.4 Modelling of Stenting 4717.2.5 Basics of Modelling 4727.3 Multiscale Modelling of the Eye 4747.4 Pulsatile Blood Flow in the Aorta 4777.4.1 Description of the Problem 4777.5 Shape Memory Polymer Drug Delivery System 4797.6 Artificial Intelligence in Biomechanics 4837.6.1 Artificial Intelligence and Machine Learning 4837.6.2 Deep Learning 4847.6.3 Physics-Informed Neural Networks (PINNs) 4857.6.4 Biomechanical Applications of Artificial Intelligence 487References 489Index 519

O autorze

Soheil Mohammadi, PhD, is Professor of Computational Mechanics and Director of the High Performance Computing Lab in the School of Civil Engineering, University of Tehran, Iran. He has published extensively on contact mechanics, XFEM and meshless methods, multiscale physics, and related subjects.