Title:
Multiscale biomechanics : theory and applications
Author:
Mohammadi, S. (Soheil), author.
ISBN:
9781119033714
9781119033738
9781119033721
Physical Description:
1 online resource (xx, 535 pages) : illustrations (some color)
Contents:
Intro -- Multiscale Biomechanics -- Contents -- Preface -- List of Abbreviations -- Part I Introduction -- 1 Introduction -- 1.1 Introduction to Biomechanics -- 1.2 Biology and Biomechanics -- 1.3 Types of Biological Systems -- 1.3.1 Biosolids -- 1.3.2 Biofluids -- 1.3.3 Biomolecules -- 1.3.4 Synthesized Biosystems -- 1.4 Biomechanical Hierarchy -- 1.4.1 Organ Level -- 1.4.2 Tissue Level -- 1.4.3 Cellular and Lower Levels -- 1.4.4 Complex Medical Procedures -- 1.5 Multiscale/Multiphysics Analysis -- 1.6 Scope of the Book -- Part II Analytical and Numerical Bases -- 2 Theoretical Bases of Continuum Mechanics -- 2.1 Introduction -- 2.2 Solid Mechanics -- 2.2.1 Elasticity -- 2.2.2 Plasticity -- 2.2.3 Damage Mechanics -- 2.2.4 Fracture Mechanics -- 2.2.5 Viscoelasticity -- 2.2.6 Poroelasticity -- 2.2.7 Large Deformation -- 2.3 Flow, Convection and Diffusion -- 2.3.1 Thermodynamics -- 2.3.2 Fluid Mechanics -- 2.3.3 Gas Dynamics -- 2.3.4 Diffusion and Convection -- 2.4 Fluid-Structure Interaction -- 2.4.1 Lagrangian and Eulerian Descriptions -- 2.4.2 Fluid-Solid Interface Boundary Conditions -- 2.4.3 Governing Equations in the Eulerian Description -- 2.4.4 Coupled Lagrangian-Eulerian (CLE) -- 2.4.5 Coupled Lagrangian-Lagrangian (CLL) -- 2.4.6 Arbitrary Lagrangian-Eulerian (ALE) -- 3 Numerical Methods -- 3.1 Introduction -- 3.2 Finite Difference Method (FDM) -- 3.2.1 One-Dimensional FDM -- 3.2.2 Higher Order One-Dimensional FDM -- 3.2.3 FDM for Solving Partial Differential Equations -- 3.3 Finite Volume Method (FVM) -- 3.4 Finite Element Method (FEM) -- 3.4.1 Basics of FEM Interpolation -- 3.4.2 FEM Basis Functions/Shape Functions -- 3.4.3 Properties of the Finite Element Interpolation -- 3.4.4 Physical and Parametric Coordinate Systems -- 3.4.5 Main Types of Finite Elements -- 3.4.6 Governing Equations of the Boundary Value Problem.
3.4.7 Numerical Integration -- 3.5 Extended Finite Element Method (XFEM) -- 3.5.1 A Review of XFEM Development -- 3.5.2 Partition of Unity -- 3.5.3 Enrichments -- 3.5.4 Signed Distance Function -- 3.5.5 XFEM Approximation for Cracked Elements -- 3.5.6 Boundary Value Problem for a Cracked Body -- 3.5.7 XFEM Discretisation of the Governing Equation -- 3.5.8 Numerical Integration -- 3.5.9 Selection of Enrichment Nodes for Crack Propagation -- 3.5.10 Incompatible Modes of XFEM Enrichments -- 3.5.11 The Level Set Method for Tracking Moving Boundaries -- 3.5.12 XFEM Tip Enrichments -- 3.5.13 XFEM Enrichment Formulation for Large Deformation Problems -- 3.6 Extended Isogeometric Analysis (XIGA) -- 3.6.1 Introduction -- 3.6.2 Isogeometric Analysis -- 3.6.3 Extended Isogeometric Analysis (XIGA) -- 3.6.4 XIGA Governing Equations -- 3.6.5 Numerical Integration -- 3.7 Meshless Methods -- 3.7.1 Why Going Meshless -- 3.7.2 Meshless Approximations -- 3.7.3 Meshless Solutions for the Boundary Value Problems -- 3.8 Variable Node Element (VNE) -- 4 Multiscale Methods -- 4.1 Introduction -- 4.2 Homogenization Methods -- 4.2.1 Introduction -- 4.2.2 Representative Volume Element (RVE) -- 4.2.3 Mathematical Homogenization -- 4.2.4 Computational Homogenization -- 4.3 Molecular Dynamics (MD) -- 4.3.1 Introduction -- 4.3.2 Statistical Mechanics -- 4.3.3 MD Equations of Motion -- 4.3.4 Models for Atomic Interactions -- MD Potentials -- 4.3.5 Measures for Determining the State of MD Systems -- 4.3.6 Stress Computation in MD -- 4.3.7 Molecular Statics -- 4.3.8 Sample MD Simulation of a Polymer -- 4.4 Sequential Multiscale Method -- 4.4.1 Introduction -- 4.4.2 Multiscale Modelling of CNT Reinforced Concrete -- 4.4.3 Molecular Dynamics Simulation of CNTs -- 4.4.4 Simulation of CNT-Reinforced Calcium Silicate Hydrate -- 4.4.5 Micromechanical Simulation of CNT-Reinforced Cement.
4.4.6 Mesoscale Simulation of CNT-Reinforced Concrete -- 4.4.7 Macroscale Simulation of CNT-Reinforced Concrete -- 4.5 Concurrent Multiscale Methods -- 4.5.1 Introduction -- 4.5.2 Quasi-Continuum Method (QC) -- 4.5.3 Bridging Domain Method (BDM) -- 4.5.4 Bridging Scale Method (BSM) -- 4.5.5 Disordered Concurrent Multiscale Method (DCMM) -- 4.5.6 Variable Node Multiscale Method (VNMM) -- 4.5.7 Enriched Multiscale Method (EMM) -- Part III Biomechanical Simulations -- 5 Biomechanics of Soft Tissues -- 5.1 Introduction -- 5.2 Physiology of Soft Tissues -- 5.2.1 Soft Tissues, Skin -- 5.2.2 Artery -- 5.2.3 Heart Leaflet -- 5.2.4 Brain Tissue -- 5.3 Hyperelastic Models of Soft Tissues -- 5.3.1 Introduction -- 5.3.2 Description of Deformation and Definition of Invariants -- 5.3.3 Isotropic neo-Hookean Hyperelastic Model -- 5.3.4 Isotropic Mooney-Rivlin Hyperelastic Model -- 5.3.5 Hyperelastic Models for Multiscale Simulation of Tendon -- 5.3.6 Anisotropic Hyperelastic Models for Fibrous Tissues -- 5.3.7 Polyconvex Undamaged Functions for Fibrous Tissues -- 5.3.8 Damaged Soft Tissue -- 5.4 Multiscale Modelling of Undamaged Tendon -- 5.4.1 Fibril Scale -- 5.4.2 Fibre Scale -- 5.4.3 Tissue Scale -- 5.5 Multiscale Analysis of a Human Aortic Heart Valve -- 5.5.1 Introduction -- 5.5.2 Organ Scale Simulation -- 5.5.3 Simulation in the Tissue Scale -- 5.5.4 Cell Scale Analysis -- 5.6 Modelling of Ligament Damage -- 5.7 Modelling of the Peeling Test: Dissection of the Medial Tissue -- 5.8 Healing in Damaged Soft Tissue -- 5.8.1 Introduction -- 5.8.2 Physical Foundation of Tissue Healing -- 5.8.3 Solution Procedure -- 5.8.4 Numerical Analysis -- 5.9 Hierarchical Multiscale Modelling of a Degraded Arterial Wall -- 5.9.1 Definition of the Problem -- 5.9.2 Multiscale Model -- 5.9.3 Hyperelastic Material Models.
5.9.4 Computational Framework of the Hierarchical Multiscale Homogenization -- 5.9.5 Numerical Results -- 5.10 Multiscale Modelling of the Brain -- 5.10.1 Introduction -- 5.10.2 Biomechanics of the Brain -- 5.10.3 Multiscale Modelling of the Brain (neo-Hookean Model) -- 5.10.4 Viscoelastic Modelling of the Brain -- 6 Biomechanics of Hard Tissues -- 6.1 Introduction -- 6.1.1 Hard Tissues -- 6.1.2 Chemical Composition of Bone -- 6.1.3 Multiscale Structure of Bone -- 6.1.4 Bone Remodelling -- 6.1.5 Contents of the Chapter -- 6.2 Concepts of Fracture Analysis of Hard Tissues -- 6.2.1 Numerical Studies of Bone Fracture -- 6.2.2 Constitutive Response of the Bone -- 6.2.3 Poroelastic Nature of Bone Tissues -- 6.2.4 Plasticity and Damage -- 6.2.5 Hyperelastic Response -- 6.3 Simulation of the Femur Bone at Multiple Scales -- 6.3.1 Microscale Simulation of the Trabecular Bone -- 6.3.2 Two-dimensional XFEM Mesoscale Fracture Simulation of the Cortical Bone -- 6.3.3 Macroscale Simulation of the Femur -- 6.4 Healing in Damaged Hard Tissue -- 6.4.1 Introduction -- 6.4.2 Physical Foundation of Bone Tissue Healing -- 6.4.3 Solution Procedure -- 6.4.4 Numerical Analysis -- 7 Supplementary Topics -- 7.1 Introduction -- 7.2 Shape Memory Alloy (SMA) Stenting of an Artery -- 7.2.1 Stenting Procedures -- 7.2.2 SMA Constitutive Equations -- 7.2.3 Contact Mechanics -- 7.2.4 Modelling of Stenting -- 7.2.5 Basics of Modelling -- 7.3 Multiscale Modelling of the Eye -- 7.4 Pulsatile Blood Flow in the Aorta -- 7.4.1 Description of the Problem -- 7.5 Shape Memory Polymer Drug Delivery System -- 7.6 Artificial Intelligence in Biomechanics -- 7.6.1 Artificial Intelligence and Machine Learning -- 7.6.2 Deep Learning -- 7.6.3 Physics-Informed Neural Networks (PINNs) -- 7.6.4 Biomechanical Applications of Artificial Intelligence -- References -- Index -- EULA.
Abstract:
"Life and space have been the most fascinating scientific concepts that I used to cogitate from my childhood; watching the "Star Trek" series or thinking on the way all living organisms have evolved from non-living atoms and molecules. As a civil engineer with numerical skills, however, it may seem quite unusual to get involved with biological problems. Nevertheless, the computational mechanics has bridged over the different pillars of science, from buildings to aerospace structures, and from spectacular suspension bridges to intelligent nano additives in biological systems. It all started about a decade ago, when my former student, Shahrokh Shahi, began his thesis endeavour on multiscale biomechanics. After his graduation, we planned for a book on the subject, although he had to separate from the project to follow his future quests. Biomechanics is primarily used to study the wide range of mechanical responses of biosystems; from biomolecules scales up to the organ and body levels, and from routine medical procedures to synthesized tissues. The wealth of well-developed mathematical and numerical methods of solving general engineering and physical problems is now available to assist the clinical staff and medical industries in assessing the existing procedures and products or to propose new engineered designs and concepts for future research and development. I have tried to provide the theoretical and computational bases of biomechanics in this textbook and to present my small contribution to encourage the young talents to further advance the numerical capabilities for analysis of biomechanical applications. The book, which can be regarded as an introduction to the multiscale biomechanics, is composed of three parts. The preliminary part is meant to provide an introduction and insight on the general concept of the biomechanics and the wide variety of biological problems that can be solved numerically through the single and multiscale methods. Part II is dedicated to analytical and numerical bases. In its first set of chapters, the general concepts of continuum mechanics associated with solid materials, fluid flow and diffusion problems are provided. The second set of chapters cover the basics of numerical analysis methods, including the finite element method, the extended finite element method, the isogeometeric analysis, the principles of meshless methods, and the variable node element. The final chapter of part II discusses the multiscale methods. It begins by examining the homogenization technique. Then, the atomistic/molecular dynamics and statistical mechanics are discussed in detail. The sequential multiscale method is thoroughly discussed by a sample case, which spans the extremely wide range of atomistic simulations, nanoscale analysis, macroscale computations, micro scale investigation and macro scale study. The multiscale chapter is concluded by the comprehensive review of the concurrent multiscale schemes. Part III is dedicated to discussions on single and multiscale biomechanical simulations. Its first chapter is devoted to the modelling of soft tissues. It begins with explaining the composition and physiology of soft tissues and their macro and micro hyperelastic constitutive laws. This chapter includes several single and multiscale simulations of soft tissue applications, including damaged tissues, aortic heart valve, skin damage, arterial wall degradation, wound healing and the viscoelastic response of brain. The next chapter of this part is dedicated to hard tissues, and briefly explains the composition of bones and the necessary mechanical models. A number of single and multiscale simulations are presented to provide more insight into the way hard tissue biomechanical studies are performed. The chapter closes by a discussion on the healing processes of hard tissues. Part III is concluded by a brief complementary chapter on a number of supplementary topics, covering the principles of stenting simulations, multiscale modelling of eye, the concept of a shape memory polymer drug delivery system and an introduction to the artificial intelligence and deep learning in biomechanical applications."-- Provided by publisher.
Local Note:
John Wiley and Sons
Genre:
Electronic Access:
https://onlinelibrary.wiley.com/doi/book/10.1002/9781119033714Copies:
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