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Non-Linear Elastic Deformations |  |
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Non-Linear Elastic Deformations | |
Acknowlegements
Preface
Chapter 1 Tensor Theory
1.1 Euclidean vector space
1.1.1 Orthonormal Bases and Components
1.1.2 Change of Basis
1.1.3 Euclidean Point Space: Cartesian Coordinates
1.2 Cartesian tensors
1.2.1 Motivation: Stress in a Continuum
1.2.2 Definition of a Cartesian Tensor
1.2.3 The Tensor Product
1.2.4 Contraction
1.2.5 Isotropic Tensors
1.3 Tensor algebra
1.3.1 Second-order Tensors
1.3.2 Eigenvalues and Eigenvectors of a Second-order Tensor
1.3.3 Symmetric Second-order Tensors
1.3.4 Antisymmetric Second-order Tensors
1.3.5 Orthogonal Second-order Tensors
1.3.6 Highter-order Tensors
1.4 Contravariant and covariant tensors
1.4.1 Reciprocal Basis. Contravariant and Covariant Components
1.4.2 Change of Basis
1.4.3 Dual Space.General Tensors
1.5 Tensor fields
1.5.1 The Gradient of a Tensor Field
1.5.2 Symbolic Notation for Differential Operators
1.5.3 Differentiation in Cartesian Coordinates
1.5.4 Differentiation in Curvilinear Coordinates
1.5.5 Curves and Surfaces
1.5.6 Integration of Tensor Fields
References
Chapter 2 Analysis of Deformation and Motion
2.1 Kinematics
2.1.1 Observers and Frames of Reference
2.1.2 Configurations and Motions
2.1.3 Reference Configuratins and Deformations
2.1.4 Rigid-body Motions
2.2 Analsis of deformation and strain
2.2.1 The Deformation Gradient
2.2.2 Deformation of Volume and Surface
2.2.3 "Strain, Stretch, Extension and Shear"
2.2.4 Polar Decomposition of the Deformation Gradient
2.2.5 Geometrical Interpretations of the Deformation
2.2.6 Examples of Deformations
2.2.7 Strain Tensors
2.2.8 Change of Reference Configuration or Observer
2.3 Analysis of motion
2.3.1 Deformation and Strain Rates
2.3.2 Spins of the Lagrangean an Eulerian Axes
2.4 Objectivity of tensor fields
2.4.1 Eulerian and Lagrangean Objectivity
2.4.2 Embedded components of tensors
References
"Chapter 3 Balance Laws, Stress and Field Equations"
3.1 Mass conservation
3.2 Momentum balance equations
3.3 The Cauchy stress tensor
3.3.1 Linear Dependence of the Stress Vector on the Surface Normal
3.3.2 Cauchy's Laws of Motion
3.4 The nominal stress tensor
3.4.1 Definition of Nominal Stress
3.4.2 The Lagrangean Field Equations
3.5 Conjugate stress analysis
3.5.1 Work Rate and Energy Balance
3.5.2 Conjugage Stress Tensors
3.5.3 Stress Rates
References
Chapter 4 Elasticity
4.1 Constitutive laws for simple materials
4.1.1 General Remarks on Constitutive Laws
4.1.2 Simple Materials
4.1.3 Material Uniformity and Homogeneity
4.2 Cauchy elastic materials
4.2.1 The Constitutive Equation for a Cauchy Elastic Material
4.2.2 Alternative Forms of the Constitutive Equation
4.2.3 Material Symmetry
4.2.4 Undistorted Configurations and Isotropy
4.2.5 Anisotropic Elastic Solids
4.2.6 Isotropic Elastic Solids
4.2.7 Internal Constraints
4.2.8 Differentiation of a Scalar Function of a Tensor
4.3 Green elastic materials
4.3.1 The Strain-Energy Function
4.3.2 Symmetry Groups for Hyperelastic Materials
4.3.3 Stress-Deformation Relations for Constrained Hyperelastic Materials
4.3.4 Stress-Deformation Relations for Isotropic Elastic Materials
4.3.5 Strain-Energy Functions for Isotropic Elastic Materials
4.4 Application to simple homogeneous deformations
References
Chapter 5 Boundary-Value Problems
5.1 Formulation of boundary-value problems
5.1.1 Equations of Motion and Equilibrium
5.1.2 Boundary Conditions
5.1.3 Restrictions on the Deformation
5.2 Problems for unconstrained materials
5.2.1 Ericksen's Theorem
5.2.2 Spherically Symmetric Deformation of a Spherical Shell
5.2.3 Extension and Inflation of a Circular Cylindrical Tube
5.2.4 Bending of a Rectangular Block into a Sector of a Circular Tube
5.2.5 Combined Extension and Torsion of a Solid Circular Cylinder
5.2.6 Plane Strain Problems: Complex Variable Methods
5.2.7 Growth Conditions
5.3 Problems for materials with internal constrainsts
5.3.1 Preliminaries
5.3.2 Spherically Symmetric Deformation of a Spherical Shell
5.3.3 Combined Extension and Inflation of a Circular Cylindrical Tube
5.3.4 Flexure of a Rectangular Block
5.3.5 Extension and Torsion of a Circular Cylinder
5.3.6 Shear of a Circular Cylindrical Tube
5.3.7 Rotation of a Solid Circular Cylinder about its Axis
5.4 Variational principles and conservation laws
5.4.1 Virtual Work and Related Principles
5.4.2 The Principle of Stationary Potential Energy
5.4.3 Complementary and Mixed Variational Principles
5.4.4 Variational Principles with Constraints
5.4.5 Conservation Laws and the Energy Momentum Tensor
References
Chapter 6 Incremental Elastic Deformations
6.1 Incremental constitutive relations
6.1.1 Deformation Increments
6.1.2 Stress Increments and Elastic Moduli
6.1.3 Instantaneous Moduli
6.1.4 Elastic Moduli for Isotropic Materials
6.1.5 Elastic Moduli for Incompressible Isotropic Materials
6.1.6 Linear and Second-order Elasticity
6.2 Structure and properties of the incremental equations
6.2.1 Incremental Boundary-Value Problems
6.2.2 Uniqueness: Global Considerations
6.2.3 Incremental Uniqueness and Stability
6.2.4 Variational Aspects of Incremental Problems
6.2.5 Bifurcation Analysis: Dead-load Tractions
6.2.6 Bifurcation Analysis: Non-adjoint and Self-adjoint Data
6.2.7 The Strong Ellipticity Condition
6.2.8 Constitutive Branching and Constitutive Inequalities
6.3 Solution of incremental boundary-value problems
6.3.1 Bifurcation of a Pre-strained Rectangular Block
6.3.2 Global Aspects of the Plane-strain Bifurcation of a Rectangular Block
6.3.3 Other Problems with Underlying Homogenous Deformation
6.3.4 Bifurcation of a Pressurized Spherical Shell
6.4 Waves and vibrations
References
Chapter 7 Elastic Properties of Sold Materials
7.1 Phenomenological theory
7.2 Isotropic materials
7.2.1 Homogenous Pure Strain of an Incompressible Material
7.2.2 Application to Rubberlike Materials
7.2.3 Homogeneous Pure Strain of a Compressible Material
7.3 The effect of small changes in material properties
7.4 Nearly incompressible materials
7.4.1 Compressible Materials and the Incompressible Limit
7.4.2 Nearly Incompressible Materials
7.4.3 Pure Homogeneous Strain of a Nearly Incompressible Isotropic Material
7.4.4 Application to Rubberlike Materials
References
Appendix I Convex Functions
References
Appendix 2 Glossary of symbols
网友对Non-Linear Elastic Deformations的评论
值得保留一本，经典老书
This is great book for someone who knows elasticity and some continuum mechanics. recommended for graduate students who will pursue research requiring nonlinear elasticity. For average course on elasticity, this might not be the best book.
The book arrived on time, was professionally wrapped, and its condition fully corresponded to the vendor's description. To summarize: a fantastic experience at fantastic_shopping.
This is one of the best contemporary books in solid mechanics. This is the book for people who have read other continuum mechanics/elasticity books and wondered "but why?". You really should be motivated and solve the problems too. Every line of the book is written for a purpose. I find something new every time I read it. If you don't understand something on first try, go on to the next section and return later.
Prof. Ogden is a mathematician. But for a mathematician, his book is very physically motivated. He also gives physical interpretation for most of the mathematical results he derives. The cute part of this book is, although this book is more mathematical than most books engineers would read, it looks like Ogden wants to also flaunt his mathematical credentials. He gives a physical definition in the body of the book and provides a corresponding abstract mathematical definition in the footnotes.
If you are interested in finite deformation and hyperelasticity and constitutive relations, this is the book. The distinction he makes between Cauchy and Green elasticity is one of the good one I have come across.
This is not for undergraduates (unless one has a very good mechanics and mathematics background). I doubt if it is suitable as a first graduate book either. As a second graduate course or for self study after a course in elasticity/continuum mechanics/solid mechanics, this book is a gem!
It is easy to see why other reviewers do not like this book: it is very advanced. It is not for an undergraduate, and probably not for a graduate student unless she or he is already very familiar with elasticity and solid mechanics. It is not, at bottom, a text for learning the rudiments of the theory of elasticity: it is more on the level of a research monograph, and Malvern or Fung are better choices for many students. However, Ogden is probably the best work available (other than perhaps Truesdell, who can be an acquired taste) on the rigourous theory of non-linear elasticity. If you have an interest in the structure of constitutive relations, need a rigourous mathematical reference for finite element modeling, or are interested in exploring the assumptions and limitations of the linearised theory of elasticity, Ogden is not just the best place to start, but possibly the only place to go.
Holzapfel covers the same topics (rubber elasticity) and is an easier read with only slightly less rigor. That said, I do agree with a previous reviewer (Temesgen), who said that this Ogden text is for those who've read books like Holzapfel and still wonder "but why?" about a certain topic. My "but why?" question had to do with improving my understanding of the underlying assumptions in the popular rubber models (e.x. where does the Mooney-Rivlin strain-energy function actually come from?) -- Prof Ogden did not disappoint. Oh, and if you're interested in the famous "Ogden" material model, this text will have what you're looking for... needless-to-say..
Two big negatives to this text: 1) it doesn't have the more modern material models (obviously -- e.x. Yeoh) and 2) the math jargon is a little much for me -- but I've seen much "worse."
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