Continuum Mechanics for Engineers, Third Edition

CONTINUUM THEORY
The Continuum Concept
Continuum Mechanics
Applications for Continuum Mechanics
ESSENTIAL MATHEMATICS
Scalars, Vectors and Cartesian Tensors
Tensor Algebra in Symbolic Notation-Summation Convention
Indicial Notation
Matrices and Determinants
Transformation of Cartesian Tensors
Principal Values and Principal Directions of Symmetric Second-Order Tensors
Tensor Fields, Tensor Calculus
Integral Theorems of Gauss and Stokes
Problems
STRESS PRINCIPLES
Body and Surface Forces; Mass Density
Cauchy Stress Principle
The Stress Tensor
Force and Moment Equilibrium; Stress Tensor Symmetry
Stress Transformation Laws
Principal Stresses; Principal Stress Directions
Maximum and Minimum Stress Values
Mohr's Circles for Stress
Plane Stress
Deviator and Spherical Stress States
Octahedral Shear Stress
Problems
KINEMATICS OF DEFORMATION AND MOTION
Particles, Configurations, Deformation, and Motion
Material and Spatial Coordinates
Lagrangian and Eulerian Descriptions
The Displacement Field
The Material Derivative
Deformation Gradients, Finite Strain Tensors
Infinitesimal Deformation Theory
Stretch Ratios
Rotation Tensor, Stretch Tensors
Velocity Gradient, Rate of Deformation, Vorticity
Material Derivative of Line Elements, Area, Volumes
Problems
FUNDAMENTAL LAWS AND EQUATIONS
Balance Laws, Field Equations, Constitutive Equations
Material Derivatives of Line, Surface and Volume Integrals
Conservation of Mass, Continuity Equation
Linear Momentum Principle, Equations of Motion
The Piola-Kirchhoff Stress Tensors, Lagrangian Equations of Motion
Moment of Momentum (Angular Momentum) Principle
Law of Conservation of Energy, The Energy Equation
Entropy and the Clausius-Duhem Equation
Restrictions on Elastic Materials by the Second Law of Thermodynamics
Invariance
Restrictions on Constitutive Equations from Objectivity
Constitutive Equations
References
Problems
LINEAR ELASTICITY
Elasticity, Hooke's Law, Strain Energy
Hooke's Law for Isotropic Media, Elastic Constants
Elastic Symmetry, Hooke's Law for Anisotropic Media
Isotropic Elastostatics and Elastodynamics, Superposition Principle
Plane Elasticity
Linear Thermoelasticity
Airy Stress Function
Torsion
Three Dimensional Elasticity
Problems
FLUIDS
Viscous Stress Tensor, Stokesian and Newtonian Fluids
Basic Equations of Viscous Flow, Navier-Stokes Equations
Specialized Fluids
Steady Flow, Irrotational Flow, Potential Flow
The Bernoulli Equation, Kelvin's Theorem
Problems
NONLINEAR ELASTICITY
Molecular Approach to Rubber Elasticity
A Strain Energy Theory for Nonlinear Elasticity
Specific Forms of the Strain Energy
Exact Solution for an Incompressible Neo-Hookean Material
References
Problems
LINEAR VISCOELASTICITY
Introduction
Viscoelastic Constitutive Equations in Linear Differential Operator Form
One-Dimensional Theory, Mechanical Models
Creep and Relaxation
Superposition Principle, Hereditary Integrals
Harmonic Loadings, Complex Modulus, and Complex Compliance
Three-Dimensional Problems, The Correspondence Principle
References
Problems
Index