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MULTISCALE BIOMECHANICS
Model biomechanical problems at multiple scales with this cutting-edge technology
Multiscale modelling is the set of techniques used to solve physical problems which exist at multiple scales either in space or time. It has been shown to have significant applications in biomechanics, the study of biological systems and their structures, which exist at scales from the macroscopic to the microscopic and beyond, and which produce a myriad of overlapping problems. The next generation of biomechanical researchers therefore has need of the latest multiscale modelling techniques.
Multiscale Biomechanics offers a comprehensive introduction to these techniques and their biomechanical applications. It includes both the theory of multiscale biomechanical modelling and its practice, incorporating some of the latest research and surveying a wide range of multiscale methods. The result is a thorough yet accessible resource for researchers looking to gain an edge in their biomechanical modelling.
Multiscale Biomechanics readers will find:
* Practical biomechanical applications for a variety of multiscale methods
* Detailed discussion of soft and hard tissues, and more
* An introduction to analysis of advanced topics ranging from stenting, drug delivery systems, and artificial intelligence in biomechanics
Multiscale Biomechanics is a useful reference for researchers and scientists in any of the life sciences with an interest in biomechanics, as well as for graduate students in mechanical, biomechanical, biomedical, civil, material, and aerospace engineering.
List of contents
Contents
Preface xiii
List of Abbreviations xvii
Part I Introduction 1
1 Introduction 3
1.1 Introduction to Biomechanics 3
1.2 Biology and Biomechanics 3
1.3 Types of Biological Systems 6
1.3.1 Biosolids 6
1.3.2 Biofluids 7
1.3.3 Biomolecules 8
1.3.4 Synthesized Biosystems 9
1.4 Biomechanical Hierarchy 10
1.4.1 Organ Level 10
1.4.2 Tissue Level 11
1.4.3 Cellular and Lower Levels 12
1.4.4 Complex Medical Procedures 13
1.5 Multiscale/Multiphysics Analysis 13
1.6 Scope of the Book 17
Part II Analytical and Numerical Bases 21
2 Theoretical Bases of Continuum Mechanics 23
2.1 Introduction 23
2.2 Solid Mechanics 23
2.2.1 Elasticity 24
2.2.2 Plasticity 28
2.2.3 Damage Mechanics 31
2.2.4 Fracture Mechanics 36
2.2.5 Viscoelasticity 53
2.2.6 Poroelasticity 59
2.2.7 Large Deformation 63
2.3 Flow, Convection and Diffusion 72
2.3.1 Thermodynamics 72
2.3.2 Fluid Mechanics 74
2.3.3 Gas Dynamics 78
2.3.4 Diffusion and Convection 81
2.4 Fluid-Structure Interaction 83
2.4.1 Lagrangian and Eulerian Descriptions 83
2.4.2 Fluid-Solid Interface Boundary Conditions 84
2.4.3 Governing Equations in the Eulerian Description 85
2.4.4 Coupled Lagrangian-Eulerian (CLE) 86
2.4.5 Coupled Lagrangian-Lagrangian (CLL) 87
2.4.6 Arbitrary Lagrangian-Eulerian (ALE) 88
3 Numerical Methods 93
3.1 Introduction 93
3.2 Finite Difference Method (FDM) 93
3.2.1 One-Dimensional FDM 94
3.2.2 Higher Order One-Dimensional FDM 95
3.2.3 FDM for Solving Partial Differential Equations 98
3.3 Finite Volume Method (FVM) 99
3.4 Finite Element Method (FEM) 102
3.4.1 Basics of FEM Interpolation 102
3.4.2 FEM Basis Functions/Shape Functions 103
3.4.3 Properties of the Finite Element Interpolation 105
3.4.4 Physical and Parametric Coordinate Systems 106
3.4.5 Main Types of Finite Elements 106
3.4.6 Governing Equations of the Boundary Value Problem 109
3.4.7 Numerical Integration 112
3.5 Extended Finite Element Method (XFEM) 113
3.5.1 A Review of XFEM Development 113
3.5.2 Partition of Unity 114
3.5.3 Enrichments 115
3.5.4 Signed Distance Function 115
3.5.5 XFEM Approximation for Cracked Elements 115
3.5.6 Boundary Value Problem for a Cracked Body 117
3.5.7 XFEM Discretisation of the Governing Equation 118
3.5.8 Numerical Integration 119
3.5.9 Selection of Enrichment Nodes for Crack Propagation 121
3.5.10 Incompatible Modes of XFEM Enrichments 122
3.5.11 The Level Set Method for Tracking Moving Boundaries 123
3.5.12 XFEM Tip Enrichments 124
3.5.13 XFEM Enrichment Formulation for Large Deformation Problems 132
3.6 Extended Isogeometric Analysis (XIGA) 133
3.6.1 Introduction 133
3.6.2 Isogeometric Analysis 133
3.6.3 Extended Isogeometric Analysis (XIGA) 136
3.6.4 XIGA Governing Equations 138
3.6.5 Numerical Integration 140
3.7 Meshless Methods 142
3.7.1 Why Going Meshless 142
3.7.2 Meshless Approximations 143
3.7.3 Meshless Solutions for the Boundary Value Problems 158
3.8 Variable Node Element (VNE) 166
4 Multiscale Methods 171
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About the author
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.
