Continuum Mechanics for Engineers, Third Edition provides engineering students with a complete, concise, and accessible introduction to advanced engineering mechanics. The impetus for this latest edition was the need to suitably combine the introduction of continuum mechanics, linear and nonlinear elasticity, and viscoelasticity for a graduate-level course sequence. An outgrowth of course notes and problems used to teach these subjects, the third edition of this bestselling text explores the basic concepts behind these topics and demonstrates their application in engineering practice.
Presents Material Consistent with Modern Literature
A new rearranged and expanded chapter on elasticity more completely covers Saint-Venant’s solutions. Subsections on extension, torsion, pure bending and flexure present an excellent foundation for posing and solving basic elasticity problems. The authors’ presentation enables continuum mechanics to be applied to biological materials, in light of their current importance. They have also altered the book’s notation―a common struggle for many students―to better align it with modern continuum mechanics literature. This book addresses students’ need to understand the sophisticated simulation programs that use nonlinear kinematics and various constitutive relationships. It includes an introduction to problem solution using MATLAB®, emphasizing this language’s value in enabling users to stay focused on fundamentals.
This book provides information that is useful in emerging engineering areas, such as micro-mechanics and biomechanics. With an abundance of worked examples and chapter problems, it carefully explains necessary mathematics as required and presents numerous illustrations, giving students and practicing professionals an excellent self-study guide to enhance their skills. Through a mastery of this volume’s contents and additional rigorous finite element training, they will develop the mechanics foundation necessary to skillfully use modern, advanced design tools.
Continuum Theory
Continuum Mechanics
Starting Over
Notation
Essential Mathematics
Scalars, Vectors and Cartesian Tensors
Tensor Algebra in Symbolic Notation - Summation Convention
Indicial Notation
Matrices and Determinants
Transformations of Cartesian Tensors
Principal Values and Principal Directions
Tensor Fields, Tensor Calculus
Integral Theorems of Gauss and Stokes
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
Kinematics of Deformation and Motion
Particles, Configurations, Deformations and Motion
Material and Spatial Coordinates
Langrangian and Eulerian Descriptions
The Displacement Field
The Material Derivative
Deformation Gradients, Finite Strain Tensors
Infinitesimal Deformation Theory
Compatibility Equations
Stretch Ratios
Rotation Tensor, Stretch Tensors
Velocity Gradient, Rate of Deformation, Vorticity
Material Derivative of Line Elements, Areas, Volumes
Fundamental Laws and Equations
Material Derivatives of Line, Surface, and Volume Integrals
Conservation of Mass, Continuity Equation
Linear Momentum Principle, Equations of Motion
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
The General Balance Law
Restrictions on Elastic Materials by the Second Law of Thermodynamics
Invariance
Restrictions on Constitutive Equations from Invariance
Constitutive Equations
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
Saint-Venant Problem
Plane Elasticity
Airy Stress Function
Linear Thermoelasticity
Three-Dimensional Elasticity
Classical 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
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
Linear Viscoelasticity
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
Appendices
Index
