Continuum Mechanics of Anisotropic Materials

TRAMA

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.

SOMMARIO

Chapter 1. Introduction Chapter 2. Mechanical modeling of materials 2.1 Introduction2.2 Models and the real physical world2.3 Guidelines for modeling objects and solving mechanics problems2.4 The types of models used in mechanics2.5 The particle model2.6 The rigid object model2.7 The deformable continuum model 2.8 Lumped parameter models 2.9 Statistical models2.10 Cellular automata2.11 The limits of reductionism2.12 ReferencesAppendix 2A Laplace transform refresherAppendix 2B First order differential equationsAppendix 2C Electrical analogs of the spring and dashpot modelsChapter 3. Basic continuum kinematics3.1 The deformable material model, the continuum3.2 Rates of change and the spatial representation of motion3.3 Infinitesimal motions3.4 The strain conditions of compatibilityChapter 4. Continuum formulations of conservation laws 4.1 The conservation principles4.2 The conservation of mass4.3 The state of stress at a point4.4 The stress equations of motion4.5 The conservation of energyChapter 5. Formulation of constitutive equations 5.1 Guidelines for the formulation of constitutive equations5.2 Constitutive ideas5.3 Localization5.4 Invariance under rigid object motions5.5 Determinism5.6 Linearization5.7 Coordinate invariance5.8 Homogeneous versus inhomogeneous constitutive models5.9 Restrictions due to material symmetry5.10 The symmetry of the material coefficient tensors5.11 Restrictions on the coefficients representing material properties5.12 Summary of results5.13 Relevant literature Chapter 6 Modeling material symmetry 6.1 Introduction 6.2 The representative volume element (RVE)6.3 Crystalline materials and textured materials6.4 Planes of mirror symmetry6.5 Characterization of material symmetries by planes of symmetry6.6 The forms of the 3D symmetric linear transformation A 6.7 The forms of the 6D symmetric linear transformation 6.8 Curvilinear anisotropy6.9 Symmetries that permit chirality6.10 Relevant literature Chapter 7. Four linear continuum theories 7.1 Formation of continuum theories7.2 The theory of fluid flow through rigid porous media7.3 The theory of elastic solids7.4 The theory of viscous fluids7.5 The theory of viscoelastic materials7.6 Relevant literature Chapter 8 Modeling material microstructure 8.1 Introduction 8.2 The representative volume element (RVE)8.3 Effective material parameters8.4 Effective elastic constants8.5 Effective permeability8.6 Structural gradients8.7 Tensorial representations of microstructure 8.8 Relevant literature Chapter 9. Poroelasticity 9.1 Poroelastic materials9.2 The stress-strain-pore pressure constitutive relation9.3 The fluid content-stress-pore pressure constitutive relation9.4 Darcy’s Law9.5 Matrix material and pore fluid incompressibility constraints9.6 The undrained elastic coefficients9.7 Expressions of mass and momentum conservation9.8 The basic equations of poroelasticity9.9 The basic equations of incompressible poroelasticity9.10 Some example isotropic poroelastic problems9.11 An example: the unconfined compression of an anisotropic disc9.12 Relevant literature Chapter 10 Mixture 10.1 Introduction10.2 Kinematics of mixtures10.3 The conservation laws for mixtures10.4 A statement of irreversibility in mixture processes10.5 Donnan equilibrium and osmotic pressure10.6 Continuum model for a charged porous medium; the governing equations10.7 Linear irreversible thermodynamics and the four constituent mixture10.8 Modeling swelling and compression experiments on the intervertebral disc10.9 Relevant literatureChapter 11. Kinematics and mechanics of large deformations 11.1 Large deformations11.2 Large homogeneous deformations11.3 Polar decomposition of the deformation gradients11.4 The strain measures for large deformations11.5 Measures of volume and surface change in large deformations11.6 Stress measures11.7 Finite deformation elasticity11.8 The isotropic finite deformation stress-strain relation 11.9 Finite deformation hyperelasticity11.10 Incompressible elasticity 11.11 Relevant literature Chapter 12. Plasticity Theory12.1 Extension of von Mises criterion to anisotropic materials12.2 Yield criteria for pressure sensitive anisotropic materials12.3 Some particular deformation characteristics exhibited by granular materials (dilatancy/contractancy, anisotropy, hardening/softening, and shear localization).12.4 Dilatant double shearing kinematics12.5 Evolution equations for the material parameters12.6 Numerical biaxial compression test of anisotropic granular materials12.6 Numerical triaxial compression test of anisotropic granular materials12.7 Plasticity theories for crystalline materialsAppendix A. Matrices and tensors A.1 Introduction and rationaleA.2 Definition of square, column and row matricesA.3 The types and algebra of square matricesA.4 The algebra of n-tuplesA.5 Linear transformationsA.6 Vector spacesA.7 Second rank tensorsA.8 The moment of inertia tensorA.9 The alternator and vector cross products A.10 Connection to Mohr’s circlesA.11 Special vectors and tensors in six dimensionsA.12 The gradient operator and the divergence theoremA.13 Tensor components in cylindrical coordinates

AUTORE

Stephen C. Cowin is Distinguished Professor of Mechanical Engineering at The City College of The City University of New York

ALTRE INFORMAZIONI

• Condizione: Nuovo
• ISBN: 9781489990273
• Dimensioni: 235 x 155 mm Ø 6613 gr
• Formato: Brossura
• Illustration Notes: XIII, 425 p.
• Pagine Arabe: 425
• Pagine Romane: xiii