Notes on Continuum Mechanics (eBook)

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 Hooke’s 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-Venant’s 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.