Wenbin Yu, PhD, is the Milton Clauser Professor of the School of Aeronautics and Astronautics at Purdue University. He obtained his doctorate in Aerospace Engineering from Georgia Tech in 2002. He is Chief Technology Officer of AnalySwift LLC (analyswift.com) and Director of the Composites Design and Manufacturing HUB (cdmhub.org).

• List of Figures xvList of Tables xxiForeword xxiiiPreface xxvAcknowledgments xxxiAcronyms xxxiii1 Introduction 11.1 Continuum Hypothesis 11.2 Isotropic vs. Anisotropic Materials 41.3 Homogeneous vs. Heterogeneous Materials 41.4 Materials vs. Structures 41.5 3D Structures, Plates, Shells, and Beams 61.6 Structures, Models, and Assumptions 81.7 Composite Materials 201.8 Benefits of Using Composites 241.9 Mechanics of Composite Materials 251.10 Challenges for Modeling Composites 261.11 Multiscale Modeling* 282 Mathematical Preliminaries 432.1 Scalars, Vectors, and Tensors 432.2 Cartesian Coordinate System 442.3 Index Notation 442.4 Vectors 482.5 Transformation Between Different Coordinate Systems 522.6 Second-order Tensors 552.7 Quotient Rule and Higher-order Tensors 602.8 Special Tensors 612.9 Isotropic Tensors 622.10 Tensor Calculus 622.11 General Coordinate Systems* 632.12 Calculus of Variations* 733 Theory of Anisotropic Elasticity 1033.1 Kinematics 1033.2 Kinetics 1093.3 Constitutive Relations 1143.4 Theory of Linear Elasticity 1473.5 Boundary Conditions and Continuity Conditions 1493.6 A Few Anisotropic Elasticity Problems 1513.7 Variational Principles for Anisotropic Elasticity* 1734 Micromechanics 1874.1 Introduction 1874.2 Microstructures and Their Idealizations 1884.3 Volume Average 1924.4 Effective Stiffness and Compliance 1924.5 Voigt and Reuss Rules of Mixtures 1934.6 Hybrid Rules of Mixtures 2024.7 Macro and Micro Coordinates* 2094.8 Average Stress Theorem* 2104.9 Average Strain Theorem* 2114.10 Hill–Mandel Macro-homogeneity Condition* 2134.11 Computational Homogenization* 2165 Composite Plate Models 2335.1 Introduction 2335.2 Composite Laminates 2345.3 Why Composite Plate Theories? 2365.4 Kirchhoff–Love Model Derived Using the Newtonian Method 2385.5 Reissner–Mindlin Model* 2885.6 MSG-based Composite Plate Models* 2926 Composite Beam Models* 3016.1 Introduction 3016.2 Ad Hoc Methods 3036.3 Beam Models Derived Using MSG 3196.4 A Few Composite Beam Problems 3287 Mechanics of Structure Genome* 3377.1 Introduction 3387.2 Kinematics 3397.3 Variational Statement for SG 3497.4 MSG Illustrated 3537.5 Numerical Examples 3598 Failure of Composite Materials 3718.1 Introduction 3718.2 Failure Criteria for Isotropic Materials 3748.3 Failure Criteria for Orthotropic Materials 3828.4 Strength Ratio 3998.5 Failure Envelope 4038.6 Progressive Failure Analysis 4068.7 Nonlocal Approach for Computing Strength 408Problems 409References 413Index 421

Wenbin Yu, PhD, is the Milton Clauser Professor of the School of Aeronautics and Astronautics at Purdue University. He obtained his doctorate in Aerospace Engineering from Georgia Tech in 2002. He is Chief Technology Officer of AnalySwift LLC (analyswift.com) and Director of the Composites Design and Manufacturing HUB (cdmhub.org).

• List of Figures xvList of Tables xxiForeword xxiiiPreface xxvAcknowledgments xxxiAcronyms xxxiii1 Introduction 11.1 Continuum Hypothesis 11.2 Isotropic vs. Anisotropic Materials 41.3 Homogeneous vs. Heterogeneous Materials 41.4 Materials vs. Structures 41.5 3D Structures, Plates, Shells, and Beams 61.6 Structures, Models, and Assumptions 81.7 Composite Materials 201.8 Benefits of Using Composites 241.9 Mechanics of Composite Materials 251.10 Challenges for Modeling Composites 261.11 Multiscale Modeling* 282 Mathematical Preliminaries 432.1 Scalars, Vectors, and Tensors 432.2 Cartesian Coordinate System 442.3 Index Notation 442.4 Vectors 482.5 Transformation Between Different Coordinate Systems 522.6 Second-order Tensors 552.7 Quotient Rule and Higher-order Tensors 602.8 Special Tensors 612.9 Isotropic Tensors 622.10 Tensor Calculus 622.11 General Coordinate Systems* 632.12 Calculus of Variations* 733 Theory of Anisotropic Elasticity 1033.1 Kinematics 1033.2 Kinetics 1093.3 Constitutive Relations 1143.4 Theory of Linear Elasticity 1473.5 Boundary Conditions and Continuity Conditions 1493.6 A Few Anisotropic Elasticity Problems 1513.7 Variational Principles for Anisotropic Elasticity* 1734 Micromechanics 1874.1 Introduction 1874.2 Microstructures and Their Idealizations 1884.3 Volume Average 1924.4 Effective Stiffness and Compliance 1924.5 Voigt and Reuss Rules of Mixtures 1934.6 Hybrid Rules of Mixtures 2024.7 Macro and Micro Coordinates* 2094.8 Average Stress Theorem* 2104.9 Average Strain Theorem* 2114.10 Hill–Mandel Macro-homogeneity Condition* 2134.11 Computational Homogenization* 2165 Composite Plate Models 2335.1 Introduction 2335.2 Composite Laminates 2345.3 Why Composite Plate Theories? 2365.4 Kirchhoff–Love Model Derived Using the Newtonian Method 2385.5 Reissner–Mindlin Model* 2885.6 MSG-based Composite Plate Models* 2926 Composite Beam Models* 3016.1 Introduction 3016.2 Ad Hoc Methods 3036.3 Beam Models Derived Using MSG 3196.4 A Few Composite Beam Problems 3287 Mechanics of Structure Genome* 3377.1 Introduction 3387.2 Kinematics 3397.3 Variational Statement for SG 3497.4 MSG Illustrated 3537.5 Numerical Examples 3598 Failure of Composite Materials 3718.1 Introduction 3718.2 Failure Criteria for Isotropic Materials 3748.3 Failure Criteria for Orthotropic Materials 3828.4 Strength Ratio 3998.5 Failure Envelope 4038.6 Progressive Failure Analysis 4068.7 Nonlocal Approach for Computing Strength 408Problems 409References 413Index 421

Wenbin Yu, PhD, is the Milton Clauser Professor of the School of Aeronautics and Astronautics at Purdue University. He obtained his doctorate in Aerospace Engineering from Georgia Tech in 2002. He is Chief Technology Officer of AnalySwift LLC (analyswift.com) and Director of the Composites Design and Manufacturing HUB (cdmhub.org).

• List of Figures xvList of Tables xxiForeword xxiiiPreface xxvAcknowledgments xxxiAcronyms xxxiii1 Introduction 11.1 Continuum Hypothesis 11.2 Isotropic vs. Anisotropic Materials 41.3 Homogeneous vs. Heterogeneous Materials 41.4 Materials vs. Structures 41.5 3D Structures, Plates, Shells, and Beams 61.6 Structures, Models, and Assumptions 81.7 Composite Materials 201.8 Benefits of Using Composites 241.9 Mechanics of Composite Materials 251.10 Challenges for Modeling Composites 261.11 Multiscale Modeling* 282 Mathematical Preliminaries 432.1 Scalars, Vectors, and Tensors 432.2 Cartesian Coordinate System 442.3 Index Notation 442.4 Vectors 482.5 Transformation Between Different Coordinate Systems 522.6 Second-order Tensors 552.7 Quotient Rule and Higher-order Tensors 602.8 Special Tensors 612.9 Isotropic Tensors 622.10 Tensor Calculus 622.11 General Coordinate Systems* 632.12 Calculus of Variations* 733 Theory of Anisotropic Elasticity 1033.1 Kinematics 1033.2 Kinetics 1093.3 Constitutive Relations 1143.4 Theory of Linear Elasticity 1473.5 Boundary Conditions and Continuity Conditions 1493.6 A Few Anisotropic Elasticity Problems 1513.7 Variational Principles for Anisotropic Elasticity* 1734 Micromechanics 1874.1 Introduction 1874.2 Microstructures and Their Idealizations 1884.3 Volume Average 1924.4 Effective Stiffness and Compliance 1924.5 Voigt and Reuss Rules of Mixtures 1934.6 Hybrid Rules of Mixtures 2024.7 Macro and Micro Coordinates* 2094.8 Average Stress Theorem* 2104.9 Average Strain Theorem* 2114.10 Hill–Mandel Macro-homogeneity Condition* 2134.11 Computational Homogenization* 2165 Composite Plate Models 2335.1 Introduction 2335.2 Composite Laminates 2345.3 Why Composite Plate Theories? 2365.4 Kirchhoff–Love Model Derived Using the Newtonian Method 2385.5 Reissner–Mindlin Model* 2885.6 MSG-based Composite Plate Models* 2926 Composite Beam Models* 3016.1 Introduction 3016.2 Ad Hoc Methods 3036.3 Beam Models Derived Using MSG 3196.4 A Few Composite Beam Problems 3287 Mechanics of Structure Genome* 3377.1 Introduction 3387.2 Kinematics 3397.3 Variational Statement for SG 3497.4 MSG Illustrated 3537.5 Numerical Examples 3598 Failure of Composite Materials 3718.1 Introduction 3718.2 Failure Criteria for Isotropic Materials 3748.3 Failure Criteria for Orthotropic Materials 3828.4 Strength Ratio 3998.5 Failure Envelope 4038.6 Progressive Failure Analysis 4068.7 Nonlocal Approach for Computing Strength 408Problems 409References 413Index 421