连续介质力学初级教程 第3版PDF|Epub|txt|kindle电子书版本网盘下载

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1 Introduction1

1.1 The objective of this course1

1.2 Applications to science and technology2

1.3 What is mechanics?2

1.4 A prototype of a continuum:The classical definition2

1.5 Our definition of a continuum3

1.6 The concept of stress in our definition of a continuum4

1.7 Abstract copy of a real continuum5

1.8 What is continuum mechanics about?6

1.9 Axioms of continuum mechanics7

1.10 A biological example of a hierarchy of continua depending on the size of the object involved in a scientific inquiry7

1.11 Elementary topic through which basic ideas evolved12

2 Vectors and Tensors39

2.1 Vectors39

2.2 Vector equations41

2.3 The summation convention44

2.4 Translation and rotation of coordinates49

2.5 Coordinate transformation in general53

2.6 Analytical definitions of scalars,vectors,and Cartesian tensors55

2.7 The significance of tensor equations58

2.8 Notations for vectors and tensors:Boldface or indices?58

2.9 Quotient rule59

2.10 Partial derivatives60

3 Stress64

3.1 The idea of stress64

3.2 The laws of motion66

3.3 Cauchy's formula69

3.4 Equations of equilibrium72

3.5 Change of stress components in transformation of coordinates75

3.6 Stress components in orthogonal curvilinear coordinates76

3.7 Stress boundary conditions78

4 Principal Stresses and Principal Axes88

4.1 Introduction88

4.2 Plane state of stress89

4.3 Mohr's circle for plane stress92

4.4 Mohr's circles for three-dimensional stress states94

4.5 Principal stresses94

4.6 Shearing stresses97

4.7 Stress-deviation tensor99

4.8 Lamé's stress ellipsoid102

5 Analysis of Deformation112

5.1 Deformation112

5.2 The strain115

5.3 Strain components in terms of displacements117

5.4 Geometric interpretation of infinitesimal strain components119

5.5 Infinitesimal rotation121

5.6 Finite strain components122

5.7 Principal strains:Mohr's circle124

5.8 Infinitesimal strain components in polar coordinates125

5.9 Direct derivation of the strain-displacement relations in polar coordinates128

5.10 Other strain measures131

6 Velocity Fields and Compatibility Conditions145

6.1 Velocity fields145

6.2 The compatibility condition146

6.3 Compatibility of strain components in three dimensions148

7 Constitutive Equations154

7.1 Specification of the properties of materials154

7.2 The nonviscous fluid155

7.3 Newtonian fluid156

7.4 Hookean elastic solid157

7.5 Effect of temperature161

7.6 Materials with more complex mechanical behavior161

8 Isotropy165

8.1 The concept of material isotropy165

8.2 Isotropic tensor165

8.3 Isotropic tensors of rank 3169

8.4 Isotropic tensors of rank 4170

8.5 Isotropic materials172

8.6 Coincidence of principal axes of stress and of strain172

8.7 Other methods of characterizing isotropy173

8.8 Can we recognize a material's isotropy from the microstructure?173

9 Mechanical Properties of Real Fluids and Solids181

9.1 Fluids181

9.2 Viscosity183

9.3 Plasticity of metals186

9.4 Materials with nonlinear elasticity188

9.5 Nonlinear stress-strain relationships of rubber and biological tissues191

9.6 Linear viscoelastic bodies193

9.7 Quasi-1inear viscoelasticity of biological tissues197

9.8 Non-Newtonian fluids201

9.9 Viscoplastic materials202

9.10 Sol-gel transformation and thixotropy204

10 Derivation of Field Equations209

10.1 Gauss's theorem209

10.2 Material description of the motion of a continuum212

10.3 Spatial description of the motion of a continuum214

10.4 The material derivative of a volume integral215

10.5 The equation of continuity217

10.6 The equations of motion218

10.7 Moment of momentum219

10.8 The balance of energy220

10.9 The equations of motion and continuity in polar coordinates223

11 Field Equations and Boundary Conditions in Fluid Mechanics231

11.1 The Navier-Stokes equations231

11.2 Boundary conditions at a solid-fluid interface233

11.3 Surface tension and the boundary conditions at an interface between two fluids235

11.4 Dynamic similarity and Reynolds number238

11.5 Laminar flow in a horizontal channel or tube240

11.6 Boundary layer244

11.7 Laminar boundary layer over a flat plate247

11.8 Nonviscous fluid249

11.9 Vorticity and circulation251

11.10 Irrotational flow253

11.11 Compressible nonviscous fluids254

11.12 Subsonic and supersonic flow257

11.13 Applications to biology265

12 Some Simple Problems in Elasticity270

12.1 Basic equations of elasticity for homogeneous.isotropic bodies270

12.2 Plane elastic waves272

12.3 Simplifications274

12.4 Torsion of a circular cylindrical shaft274

12.5 Beams278

12.6 Biomechanics281

13 Stress,Strain,and Active Remodeling of Structures285

13.1 Introduction285

13.2 How to discover the zero-stress state of materialin a solid body285

13.3 Remodeling the zero-stress state of a structure:A biological example of active remodeling due to change in stress288

13.4 Change of zero-stress state with temperature:Materials that“remember"their shapes290

13.5 Morphological and structural remodeling of blood vessel due to a change in blood pressure292

13.6 Remodeling of mechanical properties294

13.7 Stress analysis with the zero-stress state taken into account296

13.8 Stress-growth relationship299

Index302