Continuum Mechanics Modeling of Material Behavior

Description

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