Multiscale biomechanics /
Saved in:
Imprint: | [S.l.] : ELSEVIER, 2018. |
---|---|
Description: | 1 online resource. |
Language: | English |
Subject: | |
Format: | E-Resource Book |
URL for this record: | http://pi.lib.uchicago.edu/1001/cat/bib/11455097 |
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