Continuum Mechanics Modeling of Material Behavior

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