Multiscale biomechanics /
Multiscale Biomechanics provides new insights on multiscale static and dynamic behavior of both soft and hard biological tissues, including bone, the intervertebral disk, biological membranes and tendons. The physiological aspects of bones and biological membranes are introduced, along with micromec...
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| Other Authors: | |
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| Format: | Electronic eBook |
| Language: | English |
| Published: |
[S.l.] :
ELSEVIER,
2018.
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| Subjects: | |
| Online Access: | CONNECT |
Table of Contents:
- Intro; Title page; Table of Contents; Copyright; Introduction; I.1 Biomechanics and its scientific challenges; I.2 Motivation of the book; I.3 Organization of the book; Part 1: Theoretical Basis: Continuum Mechanics, Homogenization Methods, Thermodynamics of Growing Solid Bodies; 1: Tensor Calculus; Abstract; 1.1 A short historical vignette; 1.2 Vector spaces; 1.3 Covariant and contravariant tensors; 1.4 Linear forms and duality; 1.5 Tensor algebra; 1.6 Euclidean tensors; 1.7 Algebraic operations on tensors; 1.8 Differential calculus on tensors: tensor analysis
- 1.9 Differential operators in curvilinear coordinates1.10 Partial derivatives of function with tensor arguments; 1.11 Elements of functional analysis; 2: Continuum Mechanics; Abstract; 2.1 Motivations of nonlinear mechanics1; 2.2 Prerequisite: summary of linear elasticity; 2.3 Introduction: notion of body in a continuum description; 2.4 Kinematics: displacement, transformation gradient, strains; 2.5 Deformation tensors; 2.6 Polar decomposition theorem; 2.7 Linearization of the kinematics: small strains and small displacements; 2.8 Deformation velocities
- 2.9 Transport operations: pull-back and push-forward2.10 Isotropic tensor functions; 2.11 Stress measures and strainâ#x80;#x93;strain duality; 2.12 Balance laws; 2.13 Abbreviations, notations and nomenclature; 3: Constitutive Models of Soft and Hard Living Tissues; Abstract; 3.1 Constitutive modeling; 3.2 Isotropic elastic materials; 3.3 Elasticity tensors; 3.4 Isotropic hyperelastic materials; 3.5 Incompressible materials; 3.6 Compressible hyperelastic materials; 3.7 Isotropic compressible hyperelasticity; 3.8 Some forms of constitutive models
- 3.9 Saint-Venant Kirchhoff materials and Neo-Hookean materials through linearization3.10 Hyperviscoelastic models; 3.11 Anisotropic constitutive models: fiber reinforced solids, orthotropic materials; 3.12 Case of orthotropic materials; 3.13 Variational principles and hints to numerical solution schemes; 4: Discrete Homogenization of Network Materials; Abstract; 4.1 Introduction; 4.2 Microscopic and mesoscopic homogenization problems; 4.3 Application to trabecular bone; 5: Mechanics and Thermodynamics of Volumetric and Surface Growth; Abstract; 5.1 Introduction
- 5.2 Thermodynamics of continuous open media: a survey5.3 General balance laws accounting for mass production due to growth; 5.4 Growth kinematics and growth models; 5.5 Mechanics and thermodynamics of surface growth; 5.6 Surface growth: a review of surface thermodynamics; 5.7 Material driving forces for surface growth; 5.8 Extremum principles for biological continuum bodies undergoing volumetric and surface growth; Part 2: Multiscale Bone Mechanics; 6: Micropolar Models of Trabecular Bone; Abstract; 6.1 A survey of bone physiology; 6.2 Review of trabecular bone models
