Continuum mechanics of anisotropic materials
著者
書誌事項
Continuum mechanics of anisotropic materials
Springer, c2013
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注記
Includes bibliographical references and index
内容説明・目次
内容説明
Continuum Mechanics of Anisotropic Materials(CMAM) presents an entirely new and unique development of material anisotropy in the context of an appropriate selection and organization of continuum mechanics topics. These features will distinguish this continuum mechanics book from other books on this subject. Textbooks on continuum mechanics are widely employed in engineering education, however, none of them deal specifically with anisotropy in materials. For the audience of Biomedical, Chemical and Civil Engineering students, these materials will be dealt with more frequently and greater accuracy in their analysis will be desired. Continuum Mechanics of Anisotropic Materials' author has been a leader in the field of developing new approaches for the understanding of anisotropic materials.
目次
- Chapter 1. Introduction Chapter 2. Mechanical modeling of materials 2.1 Introduction 2.2 Models and the real physical world 2.3 Guidelines for modeling objects and solving mechanics problems 2.4 The types of models used in mechanics 2.5 The particle model 2.6 The rigid object model 2.7 The deformable continuum model 2.8 Lumped parameter models 2.9 Statistical models 2.10 Cellular automata 2.11 The limits of reductionism 2.12 References Appendix 2A Laplace transform refresher Appendix 2B First order differential equations Appendix 2C Electrical analogs of the spring and dashpot models Chapter 3. Basic continuum kinematics 3.1 The deformable material model, the continuum 3.2 Rates of change and the spatial representation of motion 3.3 Infinitesimal motions 3.4 The strain conditions of compatibility Chapter 4. Continuum formulations of conservation laws 4.1 The conservation principles 4.2 The conservation of mass 4.3 The state of stress at a point 4.4 The stress equations of motion 4.5 The conservation of energy Chapter 5. Formulation of constitutive equations 5.1 Guidelines for the formulation of constitutive equations 5.2 Constitutive ideas 5.3 Localization 5.4 Invariance under rigid object motions 5.5 Determinism 5.6 Linearization 5.7 Coordinate invariance 5.8 Homogeneous versus inhomogeneous constitutive models 5.9 Restrictions due to material symmetry 5.10 The symmetry of the material coefficient tensors 5.11 Restrictions on the coefficients representing material properties 5.12 Summary of results 5.13 Relevant literature Chapter 6 Modeling material symmetry 6.1 Introduction 6.2 The representative volume element (RVE) 6.3 Crystalline materials and textured materials 6.4 Planes of mirror symmetry 6.5 Characterization of material symmetries by planes of symmetry 6.6 The forms of the 3D symmetric linear transformation A 6.7 The forms of the 6D symmetric linear transformation 6.8 Curvilinear anisotropy 6.9 Symmetries that permit chirality 6.10 Relevant literature Chapter 7. Four linear continuum theories 7.1 Formation of continuum theories 7.2 The theory of fluid flow through rigid porous media 7.3 The theory of elastic solids 7.4 The theory of viscous fluids 7.5 The theory of viscoelastic materials 7.6 Relevant literature Chapter 8 Modeling material microstructure 8.1 Introduction 8.2 The representative volume element (RVE) 8.3 Effective material parameters 8.4 Effective elastic constants 8.5 Effective permeability 8.6 Structural gradients 8.7 Tensorial representations of microstructure 8.8 Relevant literature Chapter 9. Poroelasticity 9.1 Poroelastic materials 9.2 The stress-strain-pore pressure constitutive relation 9.3 The fluid content-stress-pore pressure constitutive relation 9.4 Darcy's Law 9.5 Matrix material and pore fluid incompressibility constraints 9.6 The undrained elastic coefficients 9.7 Expressions of mass and momentum conservation 9.8 The basic equations of poroelasticity 9.9 The basic equations of incompressible poroelasticity 9.10 Some example isotropic poroelastic problems 9.11 An example: the unconfined compression of an anisotropic disc 9.12 Relevant literature Chapter 10 Mixture 10.1 Introduction 10.2 Kinematics of mixtures 10.3 The conservation laws for mixtures 10.4 A statement of irreversibility in mixture processes 10.5 Donnan equilibrium and osmotic pressure 10.6 Continuum model for a charged porous medium
- the governing equations 10.7 Linear irreversible thermodynamics and the four constituent mixture 10.8 Modeling swelling and compression experiments on the intervertebral disc 10.9 Relevant literature Chapter 11. Kinematics and mechanics of large deformations 11.1 Large deformations 11.2 Large homogeneous deformations 11.3 Polar decomposition of the deformation gradients 11.4 The strain measures for large deformations 11.5 Measures of volume and surface change in large deformations 11.6 Stress measures 11.7 Finite deformation elasticity 11.8 The isotropic finite deformation stress-strain relation 11.9 Finite deformation hyperelasticity 11.10 Incompressible elasticity 11.11 Relevant literature Chapter 12. Plasticity Theory 12.1 Extension of von Mises criterion to anisotropic materials 12.2 Yield criteria for pressure sensitive anisotropic materials 12.3 Some particular deformation characteristics exhibited by granular materials (dilatancy/contractancy, anisotropy, hardening/softening, and shear localization). 12.4 Dilatant double shearing kinematics 12.5 Evolution equations for the material parameters 12.6 Numerical biaxial compression test of anisotropic granular materials 12.6 Numerical triaxial compression test of anisotropic granular materials 12.7 Plasticity theories for crystalline materials Appendix A. Matrices and tensors A.1 Introduction and rationale A.2 Definition of square, column and row matrices A.3 The types and algebra of square matrices A.4 The algebra of n-tuples A.5 Linear transformations A.6 Vector spaces A.7 Second rank tensors A.8 The moment of inertia tensor A.9 The alternator and vector cross products A.10 Connection to Mohr's circles A.11 Special vectors and tensors in six dimensions A.12 The gradient operator and the divergence theorem A.13 Tensor components in cylindrical coordinates
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