1st Edition
Continuum Mechanics Elasticity, Plasticity, Viscoelasticity
Most books on continuum mechanics focus on elasticity and fluid mechanics. But whether student or practicing professional, modern engineers need a more thorough treatment to understand the behavior of the complex materials and systems in use today. Continuum Mechanics: Elasticity, Plasticity, Viscoelasticity offers a complete tour of the subject that includes not only elasticity and fluid mechanics but also covers plasticity, viscoelasticity, and the continuum model for fatigue and fracture mechanics.
In addition to a broader scope, this book also supplies a review of the necessary mathematical tools and results for a self-contained treatment. The author provides finite element formulations of the equations encountered throughout the chapters and uses an approach with just the right amount of mathematical rigor without being too theoretical for practical use. Working systematically from the continuum model for the thermomechanics of materials, coverage moves through linear and nonlinear elasticity using both tensor and matrix notation, plasticity, viscoelasticity, and concludes by introducing the fundamentals of fracture mechanics and fatigue of metals. Requisite mathematical tools appear in the final chapter for easy reference.
Continuum Mechanics: Elasticity, Plasticity, Viscoelasticity builds a strong understanding of the principles, equations, and finite element formulations needed to solve real engineering problems.
Material Models
Classical Space-Time
Material Bodies
Strain
Rate of Strain
Curvilinear Coordinate Systems
Conservation of Mass
Balance of Momentum
Balance of Energy
Constitutive Equations
Thermodynamic Dissipation
Objectivity: Invariance for Rigid Motions
Coleman-Mizel Model
Fluid Mechanics
Problems for Chapter 1
Bibliography
NONLINEAR ELASTICITY
Thermoelasticity
Material Symmetries
Isotropic Materials
Incompressible Materials
Conjugate Measures of Stress and Strain
Some Symmetry Groups
Rate Formulations for Elastic Materials
Energy Principles
Geometry of Small Deformations
Linear Elasticity
Special Constitutive Models for Isotropic Materials
Mechanical Restrictions on the Constitutive Relations
Problems for Chapter 2
Bibliography
LINEAR ELASTICITY
Basic Equations
Plane Strain
Plane Stress
Properties of Solutions
Potential Energy
Special Matrix Notation
The Finite Element Method of Solution
General Equations for an Assembly of Elements
Finite Element Analysis for Large Deformations
Problems for Chapter 3
Bibliography
PLASTICITY
Classical Theory of Plasticity
Work Principle
von Mises-Type Yield Criterion
Hill Yield Criterion for Orthotropic Materials
Isotropic Hardening
Kinematic Hardening
Combined Hardening laws
General Equations of Plasticity
Strain Formulation of Plasticity
Finite Element Analysis
Large Deformations
Thermodynamics of Elastic-Plastic Materials
Problems for Chapter 4
Bibliography
VISCOELASTICITY
Linear Viscoelasticity
Effect of Temperature
Nonlinear Viscoelasticity
Thermodynamics of Materials with Fading Memory
Problems for Chapter 5
Bibliography
FRACTURE AND FATIGUE
Fracture Criterion
Plane Crack through a Sheet
Fracture Modes
Calculation of the Stress Intensity Factor
Crack Growth
Problems for Chapter 6
Bibliography
MATHEMATICAL TOOLS FOR CONTINUUM MECHANICS
Sets of Real Numbers
Matrices
Vector Analysis
Tensors
Isotropic Functions
Abstract Derivatives
Some Basic Mathematical Definitions and Theorems
Problems for Chapter 7
Bibliography
INDEX
Biography
Ellis H. Dill
