Continuum Mechanics for Engineers 4th Edition by Thomas Mase, Ronald E Smelser, Jenn Stroud Rossmann ISBN 9781482238686 1482238683

1. Continuum Theory

1.1 Chapter Learning Outcomes

1.2 Continuum Mechanics

1.3 Starting Over

1.4 Notation

2. Essential Mathematics

2.1 Chapter Learning Outcomes

2.2 Scalars, Vectors and Cartesian Tensors

2.3 Tensor Algebra in Symbolic Notation – Summation Convention

2.3.1 Kronecker Delta

2.3.2 Permutation Symbol

2.3.3 ɛ – δ Identity

2.3.4 Tensor/Vector Algebra

2.4 Indicial Notation

2.5 Matrices and Determinants

2.6 Transformations of Cartesian Tensors

2.7 Principal Values and Principal Directions of Symmetric Second-Order Tensors

2.8 Tensor Fields, Tensor Calculus

2.9 Integral Theorems of Gauss and Stokes

Problems

3. Stress Principles

3.1 Chapter Learning Outcomes

3.2 Body and Surface Forces, Mass Density

3.3 Cauchy Stress Principle

3.4 The Stress Tensor

3.5 Force and Moment Equilibrium; Stress Tensor Symmetry

3.6 Stress Transformation Laws

3.7 Principal Stresses; Principal Stress Directions

3.8 Maximum and Minimum Stress Values

3.9 Mohr’s Circles For Stress

3.10 Plane Stress

3.11 Deviator and Spherical Stress States

3.12 Octahedral Shear Stress

Problems

4. Kinematics of Deformation and Motion

4.1 Chapter Learning Outcomes

4.2 Particles, Configurations, Deformations and Motion

4.3 Material and Spatial Coordinates

4.4 Langrangian and Eulerian Descriptions

4.5 The Displacement Field

4.6 The Material Derivative

4.7 Deformation Gradients, Finite Strain Tensors

4.8 Infinitesimal Deformation Theory

4.9 Compatibility Equations

4.10 Stretch Ratios

4.11 Rotation Tensor, Stretch Tensors

4.12 Velocity Gradient, Rate of Deformation, Vorticity

4.13 Material Derivative of Line Elements, Areas, Volumes

Problems

5. Fundamental Laws and Equations

5.1 Chapter Learning Outcomes

5.2 Material Derivatives of Line, Surface, and Volume Integrals

5.3 Conservation of Mass, Continuity Equation

5.4 Linear Momentum Principle, Equations of Motion

5.5 Piola-Kirchhoff Stress Tensors, Lagrangian Equations of Motion

5.6 Moment of Momentum (Angular Momentum) Principle

5.7 Law of Conservation of Energy, The Energy Equation

5.8 Entropy and the Clausius-Duhem Equation

5.9 The General Balance Law

5.10 Restrictions on Elastic Materials by the Second Law of Thermodynamics

5.11 Invariance

5.12 Restrictions on Constitutive Equations from Invariance

5.13 Constitutive Equations

References

Problems

6. Linear Elasticity

6.1 Chapter Learning Outcomes

6.2 Elasticity, Hooke’s Law, Strain Energy

6.3 Hooke’s Law for Isotropic Media, Elastic Constants

6.4 Elastic Symmetry; Hooke’s Law for Anisotropic Media

6.5 Isotropic Elastostatics and Elastodynamics, Superposition Principle

6.6 Saint-Venant Problem

6.6.1 Extension

6.6.2 Torsion

6.6.3 Pure Bending

6.6.4 Flexure

6.7 Plane Elasticity

6.8 Airy Stress Function

6.9 Linear Thermoelasticity

6.10 Three-Dimensional Elasticity

Problems

7. Classical Fluids

7.1 Chapter Learning Outcomes

7.2 Viscous Stress Tensor, Stokesian, and Newtonian Fluids

7.3 Basic Equations of Viscous Flow, Navier-Stokes Equations

7.4 Specialized Fluids

7.5 Steady Flow, Irrotational Flow, Potential Flow

7.6 The Bernoulli Equation, Kelvin’s Theorem

Problems

8. Nonlinear Elasticity

8.1 Chapter Learning Outcomes

8.2 Nonlinear Elastic Behavior

8.3 Molecular Approach to Rubber Elasticity

8.4 A Strain Energy Theory for Nonlinear Elasticity

8.5 Specific Forms of the Strain Energy

8.6 Exact Solution for an Incompressible, Neo-Hookean Material

References

Problems

9. Linear Viscoelasticity

9.1 Chapter Learning Outcomes

9.2 Viscoelastic Constitutive Equations in Linear Differential Operator Form

9.3 One-Dimensional Theory, Mechanical Models

9.4 Creep and Relaxation

9.5 Superposition Principle, Hereditary Integrals

9.6 Harmonic Loadings, Complex Modulus, and Complex Compliance

9.7 Three-Dimensional Problems, The Correspondence Principle

References

Problems

10. Plasticity

10.1 Chapter Learning Outcomes

10.2 One-Dimensional Deformation

10.3 Modeling Plasticity

10.4 Yield Criteria

10.4.1 Tresca-Coulomb Yield Criterion

10.4.2 von Mises Yield Criterion

10.4.3 Kinematic Hardening Yield Criterion

10.5 Plastic Flow

10.5.1 Tresca-Coulomb Yield Criterion

10.5.2 von Mises Yield Criterion

10.5.3 Kinematic Hardening Yield Criterion

10.6 Plastic Modulus

10.6.1 Isotropic Hardening

10.6.2 Kinematic Hardening

10.7 Elasto-Plastic Constitutive Equations

10.7.1 Prandtl-Reuss (J2) Elasto-Plastic Equations

10.7.2 Levy-Mises Flow Equations

10.7.3 Perfectly Plastic Constitutive Behavior

10.8 Deformation Theory of Plasticity

10.9 Examples

10.9.1 Torsion of a Shaft

10.9.2 Bending of a Beam by a Moment

10.9.3 Thin-Walled Tube Tension and Torsion

References

Problems

Appendix A: General Tensors

A.1 Representation of Vectors in General Bases

A.2 The Dot Product and the Reciprocal Basis

A.3 Components of a Tensor

A.4 Determination of the Base Vectors

A.5 Derivatives of Vectors

A.5.1 Time Derivative of a Vector

A.5.2 Covariant Derivative of a Vector

A.6 Christoffel Symbols

A.6.1 Types of Christoffel Symbols

A.6.2 Calculation of the Christoffel Symbols

A.7 Covariant Derivatives of Tensors

A.8 General Tensor Equations

A.9 General Tensors and Physical Components

References

Appendix B: Viscoelastic Creep and Relaxation

Index