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Mechanics of Solids and Materials

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ISBN-10: 0521859794

ISBN-13: 9780521859790

Edition: 2006

Authors: Robert J. Asaro, Vlado A. Lubarda

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This book blends both innovative (large strain, strain rate, temperature, time dependent deformation and localized plastic deformation in crystalline solids, deformation of biological networks) and traditional (elastic theory of torsion, elastic beam and plate theories, contact mechanics) topics in a coherent theoretical framework. Extensive use of transform methods to generate solutions will make this book of interest to structural, mechanical, and aerospace engineers. Plasticity theories, micromechanics, crystal plasticity, and energetics of elastic systems are also covered, as well as an overall review of math and thermodynamics.
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Book details

Copyright year: 2006
Publisher: Cambridge University Press
Publication date: 1/16/2006
Binding: Hardcover
Pages: 880
Size: 7.25" wide x 10.00" long x 1.75" tall
Weight: 3.630
Language: English

Mathematical Preliminaries
Vectors and Tensors
Vector Algebra
Coordinate Transformation: Rotation of Axes
Second-Rank Tensors
Symmetric and Antisymmetric Tensors
Prelude to Invariants of Tensors
Inverse of a Tensor
Additional Proofs
Additional Lemmas for Vectors
Coordinate Transformation of Tensors
Some Identities with Indices
Tensor Product
Orthonormal Basis
Eigenvectors and Eigenvalues
Symmetric Tensors
Positive Definiteness of a Tensor
Antisymmetric Tensors
Orthogonal Tensors
Polar Decomposition Theorem
Polar Decomposition: Physical Approach
The Cayley-Hamilton Theorem
Additional Lemmas for Tensors
Identities and Relations Involving [down triangle, open] Operator
Suggested Reading
Basic Integral Theorems
Gauss and Stokes's Theorems
Vector and Tensor Fields: Physical Approach
Surface Integrals: Gauss Law
Evaluating Surface Integrals
The Divergence
Divergence Theorem: Relation of Surface to Volume Integrals
More on Divergence Theorem
Suggested Reading
Fourier Series and Fourier Integrals
Fourier Series
Double Fourier Series
Integral Transforms
Dirichlet's Conditions
Integral Theorems
Convolution Integrals
Fourier Transforms of Derivatives of f(x)
Fourier Integrals as Limiting Cases of Fourier Series
Dirac Delta Function
Suggested Reading
Continuum Mechanics
Kinematics of Continuum
Uniaxial Strain
Deformation Gradient
Strain Tensor
Stretch and Normal Strains
Angle Change and Shear Strains
Infinitesimal Strains
Principal Stretches
Eigenvectors and Eigenvalues of Deformation Tensors
Volume Changes
Area Changes
Area Changes: Alternative Approach
Simple Shear of a Thick Plate with a Central Hole
Finite vs. Small Deformations
Reference vs. Current Configuration
Material Derivatives and Velocity
Velocity Gradient
Deformation Rate and Spin
Rate of Stretching and Shearing
Material Derivatives of Strain Tensors: E vs. D
Rate of F in Terms of Principal Stretches
Additional Connections Between Current and Reference State Representations
Transport Formulae
Material Derivatives of Volume, Area, and Surface Integrals: Transport Formulae Revisited
Analysis of Simple Shearing
Examples of Particle and Plane Motion
Rigid Body Motions
Behavior under Superposed Rotation
Suggested Reading
Kinetics of Continuum
Traction Vector and Stress Tensor
Equations of Equilibrium
Balance of Angular Momentum: Symmetry of [sigma]
Principal Values of Cauchy Stress
Maximum Shear Stresses
Nominal Stress
Equilibrium in the Reference State
Work Conjugate Connections
Stress Deviator
Frame Indifference
Continuity Equation and Equations of Motion
Stress Power
The Principle of Virtual Work
Generalized Clapeyron's Formula
Suggested Reading
Thermodynamics of Continuum
First Law of Thermodynamics: Energy Equation
Second Law of Thermodynamics: Clausius-Duhem Inequality
Reversible Thermodynamics
Thermodynamic Relationships with p, V, T, and s
Theoretical Calculations of Heat Capacity
Third Law of Thermodynamics
Irreversible Thermodynamics
Gibbs Conditions of Thermodynamic Equilibrium
Linear Thermoelasticity
Thermodynamic Potentials in Linear Thermoelasticity
Uniaxial Loading and Thermoelastic Effect
Thermodynamics of Open Systems: Chemical Potentials
Gibbs-Duhem Equation
Chemical Potentials for Binary Systems
Configurational Entropy
Ideal Solutions
Regular Solutions for Binary Alloys
Suggested Reading
Nonlinear Elasticity
Green Elasticity
Isotropic Green Elasticity
Constitutive Equations in Terms of B
Constitutive Equations in Terms of Principal Stretches
Incompressible Isotropic Elastic Materials
Elastic Moduli Tensors
Instantaneous Elastic Moduli
Elastic Pseudomoduli
Elastic Moduli of Isotropic Elasticity
Elastic Moduli in Terms of Principal Stretches
Suggested Reading
Linear Elasticity
Governing Equations of Linear Elasticity
Elementary Theory of Isotropic Linear Elasticity
Elastic Energy in Linear Elasticity
Restrictions on the Elastic Constants
Compatibility Relations
Compatibility Conditions: Cesaro Integrals
Beltrami-Michell Compatibility Equations
Navier Equations of Motion
Uniqueness of Solution to Linear Elastic Boundary Value Problem
Potential Energy and Variational Principle
Betti's Theorem of Linear Elasticity
Plane Strain
Governing Equations of Plane Elasticity
Thermal Distortion of a Simple Beam
Suggested Reading
Elastic Beam Problems
A Simple 2D Beam Problem
Polynomial Solutions to [down triangle, open superscript 4 phi] = 0
A Simple Beam Problem Continued
Beam Problems with Body Force Potentials
Beam under Fourier Loading
Complete Boundary Value Problems for Beams
Suggested Reading
Solutions in Polar Coordinates
Polar Components of Stress and Strain
Plate with Circular Hole
Degenerate Cases of Solution in Polar Coordinates
Curved Beams: Plane Stress
Axisymmetric Deformations
Suggested Reading
Torsion and Bending of Prismatic Rods
Torsion of Prismatic Rods
Elastic Energy of Torsion
Torsion of a Rod with Rectangular Cross Section
Torsion of a Rod with Elliptical Cross Section
Torsion of a Rod with Multiply Connected Cross Sections
Bending of a Cantilever
Elliptical Cross Section
Suggested Reading
Semi-Infinite Media
Fourier Transform of Biharmonic Equation
Loading on a Half-Plane
Half-Plane Loading: Special Case
Symmetric Half-Plane Loading
Half-Plane Loading: Alternative Approach
Additional Half-Plane Solutions
Infinite Strip
Suggested Reading
Isotropic 3D Solutions
Displacement-Based Equations of Equilibrium
Boussinesq-Papkovitch Solutions
Spherically Symmetrical Geometries
Pressurized Sphere: Stress-Based Solution
Spherical Indentation
Point Forces on Elastic Half-Space
Suggested Reading
Anisotropic 3D Solutions
Point Force
Green's Function
Isotropic Green's Function
Suggested Reading
Plane Contact Problems
Wedge Problem
Distributed Contact Forces
Displacement-Based Contact: Rigid Flat Punch
Suggested Reading
Deformation of Plates
Stresses and Strains of Bent Plates
Energy of Bent Plates
Equilibrium Equations for a Plate
Shear Forces and Bending and Twisting Moments
Examples of Plate Deformation
Rectangular Plates
Suggested Reading
Dislocations and Cracks: Elementary Treatment
Tensile Cracks
Suggested Reading
Dislocations in Anisotropic Media
Dislocation Character and Geometry
Dislocations in Isotropic Media
Planar Geometric Theorem
Applications of the Planar Geometric Theorem
A 3D Geometrical Theorem
Suggested Reading
Cracks in Anisotropic Media
Dislocation Mechanics: Reviewed
Freely Slipping Crack
Crack Extension Force
Crack Faces Loaded by Tractions
Stress Intensity Factors and Crack Extension Force
Crack Tip Opening Displacement
Dislocation Energy Factor Matrix
Inversion of a Singular Integral Equation
2D Anisotropic Elasticity - Stroh Formalism
Suggested Reading
The Inclusion Problem
The Problem
Eshelby's Solution Setup
Calculation of the Constrained Fields: u[superscript c], e[superscript c], and [sigma superscript c]
Components of the Eshelby Tensor for Ellipsoidal Inclusion
Elastic Energy of an Inclusion
Inhomogeneous Inclusion: Uniform Transformation Strain
Nonuniform Transformation Strain Inclusion Problem
Inclusions in Isotropic Media
Suggested Reading
Forces and Energy in Elastic Systems
Free Energy and Mechanical Potential Energy
Forces of Translation
Interaction Between Defects and Loading Mechanisms
Elastic Energy of a Dislocation
In-Plane Stresses of Straight Dislocation Lines
Chemical Potential
Applications of the J Integral
Suggested Reading
Micropolar Elasticity
Basic Equations of Couple-Stress Elasticity
Displacement Equations of Equilibrium
Correspondence Theorem of Couple-Stress Elasticity
Plane Strain Problems of Couple-Stress Elasticity
Edge Dislocation in Couple-Stress Elasticity
Edge Dislocation in a Hollow Cylinder
Governing Equations for Antiplane Strain
Antiplane Shear of Circular Annulus
Screw Dislocation in Couple-Stress Elasticity
Configurational Forces in Couple-Stress Elasticity
Energy-Momentum Tensor of a Couple-Stress Field
Basic Equations of Micropolar Elasticity
Noether's Theorem of Micropolar Elasticity
Conservation Integrals in Micropolar Elasticity
Conservation Laws for Plane Strain Micropolar Elasticity
M Integral of Micropolar Elasticity
Suggested Reading
Thin Films and Interfaces
Dislocations in Bimaterials
Screw Dislocation Near a Bimaterial Interface
Edge Dislocation (b[subscript x]) Near a Bimaterial Interface
Edge Dislocation (b[subscript y]) Near a Bimaterial Interface
Strain Energy of a Dislocation Near a Bimaterial Interface
Suggested Reading
Strain Relaxation in Thin Films
Dislocation Array Beneath the Free Surface
Energy of a Dislocation Array
Strained-Layer Epitaxy
Conditions for Dislocation Array Formation
Frank and van der Merwe Energy Criterion
Gradual Strain Relaxation
Stability of Array Configurations
Stronger Stability Criteria
Further Stability Bounds
Suggested Reading
Stability of Planar Interfaces
Stressed Surface Problem
Chemical Potential
Surface Diffusion and Interface Stability
Volume Diffusion and Interface Stability
2D Surface Profiles and Surface Stability
Asymptotic Stresses for 1D Surface Profiles
Suggested Reading
Plasticity and Viscoplasticity
Phenomenological Plasticity
Yield Criteria for Multiaxial Stress States
Von Mises Yield Criterion
Tresca Yield Criterion
Mohr-Coulomb Yield Criterion
Gurson Yield Criterion for Porous Metals
Anisotropic Yield Criteria
Elastic-Plastic Constitutive Equations
Isotropic Hardening
Kinematic Hardening
Constitutive Equations for Pressure-Dependent Plasticity
Nonassociative Plasticity
Plastic Potential for Geomaterials
Rate-Dependent Plasticity
Deformation Theory of Plasticity
J[subscript 2] Corner Theory
Rate-Dependent Flow Theory
Elastic and Plastic Constitutive Contributions
A Rate Tangent Integration
Plastic Void Growth
Suggested Reading
Micromechanics of Crystallographic Slip
Early Observations
Other Strengthening Mechanisms
Measurements of Latent Hardening
Observations of Slip in Single Crystals and Polycrystals at Modest Strains
Deformation Mechanisms in Nanocrystalline Grains
Suggested Reading
Crystal Plasticity
Basic Kinematics
Stress and Stress Rates
Convected Elasticity
Rate-Dependent Slip
Crystalline Component Forms
Suggested Reading
The Nature of Crystalline Deformation: Localized Plastic Deformation
Perspectives on Nonuniform and Localized Plastic Flow
Localized Deformation in Single Slip
Localization in Multiple Slip
Numerical Results for Crystalline Deformation
Suggested Reading
Polycrystal Plasticity
Perspectives on Polycrystalline Modeling and Texture Development
Polycrystal Model
Extended Taylor Model
Model Calculational Procedure
Deformation Theories and Path-Dependent Response
Suggested Reading
Laminate Plasticity
Laminate Model
Additional Kinematical Perspective
Final Constitutive Forms
Suggested Reading
Mechanics of a Growing Mass
Continuity Equation
Reynolds Transport Theorem
Momentum Principles
Energy Equation
Entropy Equation
General Constitutive Framework
Multiplicative Decomposition of Deformation Gradient
Density Expressions
Elastic Stress Response
Partition of the Rate of Deformation
Elastic Moduli Tensor
Elastic Strain Energy Representation
Evolution Equation for Stretch Ratio
Suggested Reading
Constitutive Relations for Membranes
Biological Membranes
Membrane Kinematics
Constitutive Laws for Membranes
Limited Area Compressibility
Simple Triangular Networks
Suggested Reading
Solved Problems
Solved Problems for Chapters 1-33