Continuum Mechanics for Engineers, Third Edition

The second edition of this popular text continues to provide a solid, fundamental introduction to the mathematics, laws, and applications of continuum mechanics. With the addition of three new chapters and eight new sections to existing chapters, the authors now provide even better coverage of continuum mechanics basics and focus even more attention on its applications. Beginning with the basic mathematical tools needed-including matrix methods and the algebra and calculus of Cartesian tensors-the authors develop the principles of stress, strain, and motion and derive the fundamental physical laws relating to continuity, energy, and momentum. With this basis established, they move to their expanded treatment of applications, including linear and nonlinear elasticity, fluids, and linear viscoelasticity Mastering the contents of Continuum Mechanics: Second Edition provides the reader with the foundation necessary to be a skilled user of today's advanced design tools, such as sophisticated simulation programs that use nonlinear kinematics and a variety of constitutive relationships. With its ample illustrations and exercises, it offers the ideal self-study vehicle for practicing engineers and an excellent introductory text for advanced engineering students.

Table of Contents:
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