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Notes on Continuum Mechanics

Eduardo Wv Chaves|2020.08.19

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-Lame 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 Decompositi