Preface xi 1 Overview of Continuum Mechanics 1 1.1 Definition of Tensor 1 1.1.1 Vectors and Tensors 1 1.1.2 Definition of Tensors 2 1.2 Coordinate Transformations 4 1.2.
1 Summation Convention 4 1.2.2 Kronecker Increment 6 1.2.3 Coordinate Transformations 7 1.2.4 Permutation Symbols 8 1.3 Basic Operations of Tensors 9 1.
3.1 Vector Operations 9 1.3.2 Operations of Tensors 11 1.3.3 Isotropic Tensors 13 1.3.4 Tensor Functions and Calculus Operations 14 1.
3.5 Gradient, Divergence, and Curl 16 1.3.6 Green''s Theorem and Stokes'' Theorem 18 1.4 Application of Tensors in Mechanics 20 1.5 Fundamental Laws of Continuum Mechanics 21 1.5.1 Law of Conservation of Mass 21 1.
5.2 Law of Conservation of Momentum 22 1.5.3 Law of Conservation of Moment of Momentum 23 1.5.4 Law of Conservation of Energy 23 1.5.5 Second Law of Thermodynamics 25 1.
6 Constitutive Model Construction Principle 26 References 29 2 Fundamentals of Elasticity Theory 31 2.1 Fundamental Assumptions of Elasticity Theory 31 2.1.1 Continuity Assumption 32 2.1.2 Perfect Elasticity Assumption 32 2.1.3 Homogeneity Assumption 32 2.
1.4 Isotropy Assumption 33 2.1.5 Small Deformation Assumption 33 2.2 Three Fundamental Equations 34 2.2.1 Equilibrium Equations 34 2.2.
2 Geometric Equations 35 2.2.3 Physical Equations 37 2.3 Deformation and Strain 38 2.3.1 Reference Configuration and Transient Configuration 38 2.3.2 Strain Tensor 40 2.
3.3 Principal Strain and Volumetric Strain 41 2.3.4 Strain Coordination Equation 44 2.4 Stress Analysis 45 2.4.1 Cauchy Principle of Stress 45 2.4.
2 Cauchy Stress Formula 47 2.4.3 Equilibrium Different Equations and Stress Tensor Symmetry 48 2.4.4 Principal Stress and Stress Invariants 49 2.5 Foundation of the Elastic Constitutive 51 2.5.1 Elastic Constitutive Theory 51 2.
5.2 Generalized Hooke''s Law 51 References 58 3 Plastic Constitutive Theory 59 3.1 Plastic Behavior of Solid Materials 59 3.2 Variable Definitions 61 3.2.1 Decomposition of the Strain Tensor 61 3.2.2 Strain Rate and Strain Increment 62 3.
3 Drucker Postulate 64 3.3.1 Important corollary of the Drucker axioms 68 3.4 Incremental Plastic Flow Theory 71 3.5 Total Plastic Deformation Theory 79 3.6 Characteristics of Constitutive Relations in Plastic Deformation 82 References 84 4 Damage Constitutive Principles and Methods 87 4.1 Overview of Material Damage 87 4.1.
1 Continuum Damage Mechanics 87 4.1.2 Relationship Between Material Damage and Microstructure 88 4.1.3 Types of Material Damage 89 4.2 Research Methods of Damage Mechanics 90 4.3 Definition and Basic Assumptions of Damage 91 4.3.
1 Variable Selection 91 4.3.2 Definition of Damage 93 4.4 Damage Evolution Equation 95 4.4.1 State Variables 95 4.4.2 Damage Local State Principle 96 4.
4.3 Basic Principles of Irreversible Thermodynamics 96 4.4.4 Basis of Thermodynamic Damage 97 4.5 Helmholtz Free Energy (HFE) 99 4.5.1 Physical Significance of HFE 99 4.5.
2 Tensor Decomposition of HFE 99 4.5.3 Damage Criteria Based on Energy Dissipation 100 References 101 5 Basics of Micromechanics 103 5.1 Basic Concepts of Micromechanics 103 5.1.1 Introduction to Representative Volume Elements 104 5.1.2 Localization 105 5.
2 Eshelby Eigenstrain Theory and Equivalent Inclusion Theory 107 5.2.1 Eigenstrain Theory 107 5.2.2 Equivalent Inclusion Theory 112 5.3 Hill Theorem 114 5.4 Mean Field Method Based on Eshelby Equivalent Inclusion Theory 115 5.4.
1 Basic Process of Homogenization Method 115 5.4.2 Sparse Methods 118 5.4.3 Mori-Tanaka Method 119 5.4.4 Self-consistent Method for Polycrystalline Materials 121 References 121 6 Numerical Implementation of Constitutive Relations 123 6.1 Basic Concepts 123 6.
1.1 Numerical Solution of Differential Equations 123 6.1.2 Newton''s Iterative Method 125 6.1.3 One-dimensional Elastoplastic Constitutive Model 127 6.1.4 Rate Form of the Stress-Strain Relationship 128 6.
1.5 Stress-Strain Relationship with Kinematic Hardening in Rate Form 129 6.1.6 Incremental Form of the Governing Equations 130 6.1.7 Elastic Predictor/Plastic Corrector Solution Algorithm 131 6.1.8 Consistent Elastoplastic Modulus 134 6.
2 Three-dimensional Elastoplastic Model and Numerical Solution Framework 136 6.2.1 Model Overview 136 6.2.2 Stress-Strain Rate Relations 138 6.2.3 Elastic Predictor/Plastic Corrector Solution Algorithm 139 6.2.
4 Consistency Elastoplastic Modulus 142 6.3 Three-dimensional Elastoviscoplastic Model with Yield Surface and Solution Framework 142 6.3.1 Model Overview 142 6.3.2 The Definition of the Plastic Multiplier 143 6.3.3 Elastic Predictor/Plastic Corrector Solution Algorithm 144 6.
4 Three-dimensional Elastoplastic Damage Model and Solution Framework 147 6.4.1 Model Overview 147 6.4.2 Elastic Prediction/Plastic Correction-based Solution Algorithm 148 6.4.3 Numerical Issues 149 6.5 Custom Constitutive Models Based on ABAQUS 150 6.
6 Conclusion 152 References 152 7 Artificial Intelligence in Constitutive Research 153 7.1 Tensor Bases of Machine Learning 153 7.1.1 Function of Tensor in Machine Learning Algorithms 153 7.1.2 Key Operational Rule of Tensor Application in Machine Learning 154 7.2 Basic Mathematical Principles of Artificial Intelligence 156 7.2.
1 MLP-based Machine Learning Algorithms 156 7.2.2 CART-based Machine Learning Algorithms 160 7.2.2.1 Classification and Regression Tree 161 7.2.2.
2 Ensemble CART-based Algorithm 162 7.3 Current State of Machine Learning in Research of Constative Models 163 7.3.1 Data-driven Research of the Material Constitutive Models 164 7.3.2 Machine-learning Based Prediction of Life Cycle Material Properties 165 7.3.3 Physic-informed Research of the Solid Material 166 7.
3.4 Practices to Improve the Applicability of Machine Learning Models 167 7.4 Example: Predicting Constitutive Parameters of Concrete 168 7.5 Conclusion 173 References 174 8 Tensile Creep Failure Mechanism and Theoretical Model of Sintered Nano-silver 179 8.1 Introduction 179 8.2 Molecular Dynamics Model of Sintered Neck 181 8.3 Damage Model 183 8.4 Creep Life Model 185 8.
5 Parameter Determination 185 8.6 Damage Evolution Analysis of Sintered Nano-silver 186 8.7 Theoretical Analysis of Sintered Nano-silver Creep 187 8.8 Conclusion 187 References 189 9 Unified Creep-plasticity Model for High-strength Steel and Solder Alloys 193 9.1 Introduction 193 9.2 Viscoplastic Constitutive Framework 194 9.3 Application of the Proposed Theory 199 9.3.
1 Applied to High-strength Steel 200 9.3.2 Applied to Sn-3.0Ag-0.5Cu Solder Alloy 203 9.4 Conclusion 205 References 205 10 A Multiscale Framework for the Constitutive Modeling of Rock 209 10.1 Introduction 209 10.2 Fundamentals of Rock Behavior 210 10.
2.1 Heterogeneity and Anisotropy of Rock 210 10.2.2 Mechanical Behavior Across Scales 210 10.2.3 Role of Microstructure in Governing Macroscopic Behavior 211 10.3 Multiscale Modeling Framework 211 10.3.
1 Concept of Scale Separation and Homogenization 211 10.3.2 Eshelby''s Equivalent Inclusion Theory and Effective Properties 212 10.3.3 Hill''s Incremental Method 213 10.4 Pressure Dependent Plasticity Model 215 10.4.1 Thermodynamic Formulation 215 10.
4.2 Elastoplastic Constitutive Relations 215 10.5 Application of the Multiscale Constitutive Modeling to the COx Argillite 216 10.5.1 Mineralogy and the Mechanical Response of the COx Argillite 216 10.5.2 Modelling of the Porous Clay Matrix by the extended GTN Model 217 10.6 Computational Aspects 220 10.
6.1 Local Integration Algorithm and the Consistent Tangent Moduli 220 10.6.2 Numerical Implementation of the Homogenization Procedure 222 10.7 Numerical Validations 224 10.7.1 Comparison Against FE Analysis on a Two-phase Unit Cell 224 10.7.
2 Experimental Validation 226 10.8 Conclusion 232 References 233 11 Development of a High Temperature Constitutive Model for Concrete Based on Elastoplastic Theory 235 11.1 Introduction 235 11.2 Constitutive Theory of Concrete Based on Thermodynamic Framework 235 11.2.1 Constitutive Theory of Concrete 235 11.2.2 Thermodynamic Equations 242 11.
2.3 Yield Criterion and Hardening Law 245 11.3 Damage Model of Concrete at High Temperature 250 11.3.1 External Load Damage Variables of UHPC 250 11.3.2 Heat Damage 251 11.3.
3 Determination of parameters 254 11.4 Concrete High Temperature Transient Creep Model 258 11.4.1 High Temperature Transient Creep Strain Model 258 11.4.2 Drying Deformation 260 11.4.3 Dehydration Deformation 261 11.
4.4 Chemical Decomposition 263 11.5 Model Validation 263 11.5.1 Numerical Implementation of the Constitutive Model 263 11.5.2 Numerical Model Establishment and Verification 263 11.6 Conclusion 269<.