Continuum Mechanics Modelling 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 "Continuum mechanics modeling of material behavior offers a uniquely comprehensive introduction to topics like RVE theory, fabric tensor models, micropolar elasticity, elasticity with voids, nonlocal higher gradient elasticity and damage mechanics. Contemporary continuum mechanics research has been moving into areas of complex material microstructural behavior. Graduate students who are expected to do this type of research need a fundamental background beyond classical continuum theories. The book begins with several chapters that carefully and rigorously present mathematical preliminaries: kinematics of motion and deformation; force and stress measures; and general principles of mass, momentum and energy balance. The book then moves beyond other books by dedicating several chapters to constitutive equation development, exploring a wide collection of constitutive relations and developing the corresponding material model formulations. Such material behavior models include classical linear theories of elasticity, fluid mechanics, viscoelasticity and plasticity. Linear multiple field problems of thermoelasticity, poroelasticity and electoelasticity are also presented. Discussion of nonlinear theories of solids and fluids, including finite elasticity, nonlinear/non-Newtonian viscous fluids, and nonlinear viscoelastic materials are also given. Finally, several relatively new continuum theories based on incorporation of material microstructure are presented including: fabric tensor theories, micropolar elasticity, elasticity with voids, nonlocal higher gradient elasticity and damage mechanics"--Publisher's website Annotation Contemporary continuum mechanics research has been moving into areas of complex material microstructural behaviour. Graduate students who are expected to do this type of research need a fundamental background beyond classical continuum theories. This book begins with several chapters that carefully and rigorously present mathematical preliminaries; kinematics of motion and deformation; force and stress measures; and mass, momentum and energy balance principles. It then moves beyond other books by dedicating the last chapter to constitutive equation development, exploring a wide collection of constitutive relations and developing the corresponding material model formulations