E-book
Notes on Continuum Mechanics [electronic resource] / by Eduardo W. V. Chaves.
Record details
- ISBN: 9789400759862
- Physical Description: 700 p. 220 illus. online resource.
- Publisher: Dordrecht : Springer Netherlands : 2013.
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| Subject: | Engineering. Mechanics. Materials. Engineering. Continuum Mechanics and Mechanics of Materials. Engineering Thermodynamics, Heat and Mass Transfer. Mechanics. |
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Electronic resources
| Preface | ||
| Abbreviations | ||
| Operators And Symbols | ||
| Si-Units | ||
| Introduction | ||
| 1 Mechanics | ||
| 2 What Is Continuum Mechanics | ||
| 3 Scales Of Material Studies | ||
| 4 The Initial Boundary Value Problem (Ibvp) | ||
| 1 Tensors | ||
| 1.1 Introduction | ||
| 1.2 Algebraic Operations With Vectors | ||
| 1.3 Coordinate Systems | ||
| 1.4 Indicial Notation | ||
| 1.5 Algebraic Operations With Tensors | ||
| 1.6 The Tensor-Valued Tensor Function | ||
| 1.7 The Voigt Notation | ||
| 1.8 Tensor Fields | ||
| 1.9 Theorems Involving Integrals | ||
| Appendix A: A Graphical Representation Of A Second-Order Tensor | ||
| A.1 Projecting A Second-Order Tensor Onto A Particular Direction | ||
| A.2 Graphical Representation Of An Arbitrary Second-Order Tensor | ||
| A.3 The Tensor Ellipsoid | ||
| A.4 Graphical Representation Of The Spherical And Deviatoric Parts | ||
| 2 Continuum Kinematics | ||
| 2.1 Introduction | ||
| 2.2 The Continuous Medium | ||
| 2.3 Description Of Motion | ||
| 2.4 The Material Time Derivative | ||
| 2.5 The Deformation Gradient | ||
| ^ | ||
| 2.6 Finite Strain Tensors | ||
| 2.7 Particular Cases Of Motion | ||
| 2.8 Polar Decomposition Of F | ||
| 2.9 Area And Volume Elements Deformation | ||
| 2.10 Material And Control Domains | ||
| 2.11 Transport Equations | ||
| 2.12 Circulation And Vorticity | ||
| 2.13 Motion Decomposition: Volumetric And Isochoric Motions | ||
| 2.14 The Small Deformation Regime | ||
| 2.15 Other Ways To Define Strain | ||
| 3 Stress | ||
| 3.1 Introduction | ||
| 3.2 Forces | ||
| 3.3 Stress Tensors | ||
| 4 Objectivity Of Tensors | ||
| 4.1 Introduction | ||
| 4.2 The Objectivity Of Tensors | ||
| 4.3 Tensor Rates | ||
| 5 The Fundamental Equations Of Continuum Mechanics | ||
| 5.1 Introduction | ||
| 5.2 Density | ||
| 5.3 Flux | ||
| 5.4 The Reynolds Transport Theorem | ||
| 5.5 Conservation Law | ||
| 5.6 The Principle Of Conservation Of Mass. The Mass Continuity Equation | ||
| 5.7 The Principle Of Conservation Of Linear Momentum. The Equations Of Motion | ||
| ^ | ||
| ^^ | ||
| 5.8 The Principle Of Conservation Of Angular Momentum. Symmetry Of The Cauchy Stress Tensor.- 5.9 The Principle Of Conservation Of Energy. The Energy Equation | ||
| 5.10 The Principle Of Irreversibility. Entropy Inequality | ||
| 5.11 Fundamental Equations Of Continuum Mechanics | ||
| 5.12 Flux Problems | ||
| 5.13 Fluid Flow In Porous Media (Filtration) | ||
| 5.14 The Convection-Diffusion Equation | ||
| 5.15 Initial Boundary Value Problem (Ibvp) And Computational Mechanics | ||
| 6 Introduction To Constitutive Equations | ||
| 6.1 Introduction | ||
| 6.2 The Constitutive Principles | ||
| 6.3 Characterization Of Constitutive Equations For Simple Thermoelastic Materials | ||
| 6.4 Characterization Of The Constitutive Equations For A Thermoviscoelastic Material | ||
| 6.5 Some Experimental Evidence | ||
| 7 Linear Elasticity | ||
| 7.1 Introduction | ||
| 7.2 Initial Boundary Value Problem Of Linear Elasticity | ||
| 7.3 Generalized Hookeâs Law | ||
| 7.4 The Elasticity Tensor | ||
| 7.5 Isotropic Materials | ||
| 7.6 Strain Energy Density | ||
| ^ | ||
| ^^ | ||
| 7.7 The Constitutive Law For Orthotropic Material | ||
| 7.8 Transversely Isotropic Materials | ||
| 7.9 The Saint-Venantâs And Superposition Principles | ||
| 7.10 Initial Stress/Strain | ||
| 7.11 The Navier-Lamé Equations | ||
| 7.12 Two-Dimensional Elasticity | ||
| 7.13 The Unidimensional Approach | ||
| 8 Hyperelasticity | ||
| 8.1 Introduction | ||
| 8.2 Constitutive Equations | ||
| 8.3 Isotropic Hyperelastic Materials.- 8.4 Compressible Materials | ||
| 8.5 Incompressible Materials | ||
| 8.6 Examples Of Hyperelastic Models | ||
| 8.7 Anisotropic Hyperelasticity | ||
| 9 Plasticity | ||
| 9.1 Introduction | ||
| 9.2 The Yield Criterion | ||
| 9.3 Plasticity Models In Small Deformation Regime (Uniaxial Cases) | ||
| 9.4 Plasticity In Small Deformation Regime (The Classical Plasticity Theory) | ||
| 9.5 Plastic Potential Theory | ||
| 9.6 Plasticity In Large Deformation Regime | ||
| 9.7 Large-Deformation Plasticity Based On The Multiplicative Decomposition Of The Deformation Gradient | ||
| 10 Thermoelasticity | ||
| 10.1 Thermodynamic Potentials | ||
| ^ | ||
| ^^ | ||
| 10.2 Thermomechanical Parameters | ||
| 10.3 Linear Thermoelasticity | ||
| 10.4 The Decoupled Thermo-Mechanical Problem In A Small Deformation Regime | ||
| 10.5 The Classical Theory Of Thermoelasticity In Finite Strain (Large Deformation Regime) | ||
| 10.6 Thermoelasticity Based On The Multiplicative Decomposition Of The Deformation Gradient | ||
| 10.7 Thermoplasticity In A Small Deformation Regime | ||
| 11 Damage Mechanics | ||
| 11.1 Introduction | ||
| 11.2 The Isotropic Damage Model In A Small Deformation Regime | ||
| 11.3 The Generalized Isotropic Damage Model | ||
| 11.4 The Elastoplastic-Damage Model In A Small Deformation Regime | ||
| 11.5 The Tensile-Compressive Plastic-Damage Model | ||
| 11.6 Damage In A Large Deformation Regime | ||
| 12 Introduction To Fluids | ||
| 12.1 Introduction | ||
| 12.2 Fluids At Rest And In Motion | ||
| 12.3 Viscous And Non-Viscous Fluids | ||
| 12.4 Laminar Turbulent Flow | ||
| 12.5 Particular Cases | ||
| 12.6 Newtonian Fluids | ||
| 12.7 Stress, Dissipated And Recoverable Powers | ||
| ^ | ||
| ^^ | ||
| 12.8 The Fundamental Equations For Newtonian Fluids | ||
| Bibliography | ||
| Index. | ||
| ^^ |
