Continuum Mechanics Modeling of Material Behavior

✍ Scribed by Martin H. Sadd

• Publisher: Academic Press
• Year: 2019
• Tongue: English
• Leaves: 413
• Edition: 1
• Category: Library

✦ Table of Contents

Front-Matter_2019_Continuum-Mechanics-Modeling-of-Material-Behavior
Copyright_2019_Continuum-Mechanics-Modeling-of-Material-Behavior
Preface_2019_Continuum-Mechanics-Modeling-of-Material-Behavior
Chapter-1---Introduction_2019_Continuum-Mechanics-Modeling-of-Material-Behav
Chapter 1 -
Introduction
1.1 - Materials and the Continuum Hypothesis
1.2 - Need for Tensors
1.3 - Structure of the Study
1.4 - A Little History
References
Chapter-2---Mathematical-Prelim_2019_Continuum-Mechanics-Modeling-of-Materia
Chapter 2 -
Mathematical Preliminaries
2.1 - Index and Direct Notation
2.2 - Summation Convention
2.3 - Symmetric and Antisymmetric Symbols
2.4 - Kronecker Delta and Alternating Symbol
2.5 - Determinants
2.6 - Vectors and Coordinate Frames
2.7 - Changes in Coordinate Frames: Orthogonal Transformations
2.8 - Cartesian Tensors and Transformation Laws
2.9 - Objectivity between Different Reference Frames
2.10 - Vector and Matrix Algebra
2.11 - Principal Values, Directions, and Invariants of Symmetric Second-Order Tensors
2.12 - Spherical and Deviatoric Second-Order Tensors
2.13 - Cayley–Hamilton Theorem and Matrix Polynomials
2.14 - Representation Theorems
Scalar-Valued Theorem
Tensor-Valued Theorem
Tensor-Valued Theorem with Two Arguments
2.15 - Isotropic Tensors
2.16 - Polar Decomposition Theorem
2.17 - Calculus of Cartesian Field Tensors
Divergence or Gauss Theorem
Chapter-3---Kinematics-of-Motion-and-D_2019_Continuum-Mechanics-Modeling-of-
Chapter 3 -
Kinematics of Motion and Deformation Measures
3.1 - Material Body and Motion
3.2 - Lagrangian and Eulerian Descriptions
3.3 - Material Time Derivative
3.4 - Velocity and Acceleration
3.5 - Displacement and Deformation Gradient Tensors
3.6 - Lagrangian and Eulerian Strain Tensors
3.7 - Changes in Line, Area, and Volume Elements
3.8 - Small Deformation Kinematics and Strain Tensors
3.9 - Principal Axes for Strain Tensors
3.10 - Spherical and Deviatoric Strain Tensors
3.11 - Strain Compatibility
3.12 - Rotation Tensor
3.13 - Rate of Strain Tensors
3.14 - Objective Time Derivatives
3.15 - Current Configuration as Reference Configuration
3.16 - Rivlin–Ericksen Tensors
3.17 - Curvilinear Cylindrical and Spherical Coordinate Relations
References

Chapter-4---Force-and-Stre_2019_Continuum-Mechanics-Modeling-of-Material-Beh
Chapter 4 - Force and Stress
4.1 - Body and Surface Forces
4.2 - Cauchy Stress Principle: Stress Vector
4.3 - Cauchy Stress Tensor
4.4 - Principal Stresses and Axes for Cauchy Stress Tensor
4.5 - Spherical, Deviatoric, Octahedral, and von Mises Stress
4.6 - Stress Distributions and Contour Lines
4.7 - Reference Configuration Piola–Kirchhoff Stress Tensors
4.8 - Other Stress Tensors
Kirchhoff Stress
Biot Stress
Corotational Cauchy Stress
4.9 - Objectivity of Stress Tensors
4.10 - Cylindrical and Spherical Coordinate Cauchy Stress Forms
References

Chapter-5---General-Conservation-or_2019_Continuum-Mechanics-Modeling-of-Mat
Chapter 5 - General Conservation or Balance Laws
5.1 - General Conservation Principles and the Reynolds Transport Theorem
5.2 - Conservation of Mass
5.3 - Conservation of Linear Momentum
5.4 - Conservation of Moment of Momentum
5.5 - Conservation of Linear Momentum Equations in Cylindrical and Spherical Coordinates
5.6 - Conservation of Energy
5.7 - Second Law of Thermodynamics—Entropy Inequality
5.8 - Summary of Conservation Laws, General Principles, and Unknowns
References

Chapter-6---Constitutive-relations-and-formulat_2019_Continuum-Mechanics-Mod
Chapter 6 - Constitutive relations and formulation of classical linear theories of solids and fluids
6.1 - Introduction to Constitutive Equations
6.2 - Linear Elastic Solids
6.2.1 - Constitutive Law
6.2.2 - General Formulation
6.2.2.1 - Stress formulation
6.2.2.2 - Displacement formulation
6.2.3 - Problem Solutions
6.3 - Ideal Nonviscous Fluids
6.3.1 - Constitutive Law
6.3.2 - General Formulation
6.3.3 - Problem Solutions
6.4 - Linear Viscous Fluids
6.4.1 - Constitutive Law
6.4.2 - General Formulation
6.4.3 - Problem Solutions
6.5 - Linear Viscoelastic Materials
6.5.1 - Constitutive Laws
6.5.1.1 - Analog or mechanical viscoelastic constitutive models
6.5.1.2 - Maxwell model
6.5.1.3 - Kelvin–voigt model
6.5.1.4 - More general analog models
6.5.1.5 - Linear integral constitutive relations
6.5.2 - General Formulation
6.5.2.1 - Correspondence principle
6.5.3 - Problem Solutions
6.6 - Classical Plastic Materials
6.6.1 - Yield Criteria and Constitutive Law
6.6.1.1 - Yield function
6.6.1.2 - Mises yield condition
6.6.1.3 - Tresca yield condition
6.6.1.4 - Plastic stress–strain relations
6.6.2 - Problem Solutions
References

Chapter-7---Constitutive-relations-and-formulati_2019_Continuum-Mechanics-Mo
Chapter 7 - Constitutive relations and formulation of theories involving multiple constitutive fields
7.1 - Introduction
7.2 - Thermoelastic Solids
7.2.1 - General Formulation
7.2.2 - Problem Solutions
7.2.2.1 - Cartesian coordinate formulation
7.2.2.2 - Polar coordinate formulation
7.3 - Poroelasticity
7.3.1 - Constitutive Laws and General Formulation
7.3.2 - Problem Solutions
7.4 - Electroelasticity
7.4.1 - Constitutive Laws and General Formulation
References
Chapter-8---General-Constitutive-Relations-and-F_2019_Continuum-Mechanics-Mo
Chapter 8 -
General constitutive relations and formulation of nonlinear theories of solids and fluids
8.1 - Introduction and General Constitutive Axioms
8.2 - General Simple Materials
8.3 - Nonlinear Finite Elasticity
8.3.1 - Constitutive Laws and General Formulation
8.3.2 - Problem Solutions
8.4 - Nonlinear Viscous Fluids
8.4.1 - Reiner–Rivlin Fluid
8.4.2 - Simple Incompressible Fluid
8.4.3 - Rivlin–Ericksen Fluid
8.4.4 - Viscometric Flows of Incompressible Simple Fluids
8.5 - Nonlinear Integral Viscoelastic Constitutive Models
8.5.1 - Integral Models Using a Single Deformation Tensor
8.5.2 - K-BKZ Integral Models
References

Chapter-9---Constitutive-relations-and-formulat_2019_Continuum-Mechanics-Mod
Chapter 9 -
Constitutive relations and formulation of theories incorporating material microstructure
9.1 - Introduction to Micromechanics Material Modeling
9.2 - Micropolar Elasticity
Two-dimensional couple-stress theory
9.3 - Elasticity Theory with Voids
9.4 - Doublet Mechanics
9.5 - Higher Gradient Elasticity Theories
9.6 - Fabric Theories for Granular Materials
9.7 - Continuum Damage Mechanics
References
Appendix-A---Basic-Field-Equations-in-Cartesi_2019_Continuum-Mechanics-Model
Appendix-B---Transformation-of-Field-Variables-B_2019_Continuum-Mechanics-Mo
Appendix-C---MATLAB-Primer-and-Cod_2019_Continuum-Mechanics-Modeling-of-Mate
Appendix-D---Poem_2019_Continuum-Mechanics-Modeling-of-Material-Behavior
Index_2019_Continuum-Mechanics-Modeling-of-Material-Behavior