Material Modeling and Structural Mechanics (Advanced Structured Materials, 161)

This book presents various questions of continuum mechanical modeling in the context of experimental and numerical methods, in particular, multi-field problems that go beyond the standard models of continuum mechanics. In addition, it discusses dynamic problems and practical solutions in the field of numerical methods. It focuses on continuum mechanics, which is often overlooked in the traditional division of mechanics into statics, strength of materials and kinetics. The book is dedicated to Prof. Volker Ulbricht, who passed away on April 9, 2021. Preface 7 Contents 12 List of Contributors 18 Chapter 1 The Use of the Homogenization Method in the Analysis of Anisotropic Creep in Metal-matrix Composites 22 1.1 Introduction 23 1.2 Homogenization Method for Determining the Properties of Composite Materials 29 1.3 Creep Theory of Initially Orthotropic Materials 30 1.4 Method for Determining the Average Creep Properties of Fiber Composites 32 1.5 Micromechanical Creep Analysis of Unidirectional Composite 33 1.6 Conclusions 37 References 37 Chapter 2 General Forms of Limit Surface: Application for Isotropic Materials 40 2.1 Introduction 41 2.2 Geometric Properties of Criteria 42 2.2.1 Requirements for Yield and Strength Criteria 42 2.2.2 Formulation of Yield and Strength Criteria 44 2.2.3 Pressure-sensitive Extension of Yield Criteria 47 2.3 Designation and Comparison of Yield Criteria 50 2.3.1 Nomenclature of Yield Criteria 50 2.3.2 Comparison of Yield Criteria 52 2.3.3 Shapes of Yield Criteria in the π-plane 58 2.3.4 Extreme Yield Figures 61 2.3.5 Geometric Properties and Basic Experiments 63 2.4 Yield and Strength Criteria 65 2.4.1 Recommended Yield and Strength Criteria 65 2.4.2 PODGÓRSKI-type Shape Functions 67 2.4.3 Inductive Derivation of Criteria 71 2.4.4 Modified YU Strength Theory 79 2.5 Criterion with Shape Variation in π-plane 86 2.6 Summary 87 2.7 Appendix 89 2.7.1 Invariants of Stress Tensor 89 2.7.2 Scalar Functions of Invariants 90 2.7.3 Modified Invariants 90 2.7.4 Particular Points on Limit Surface 91 2.7.5 Values for Comparison 92 2.7.6 Modified Normal Stress Hypothesis 95 2.7.7 Series of Invariants 97 2.7.8 Plausibility Assumptions 100 References 105 Chapter 3 Model Order Reduction: The Bridge Between Structural Mechanics and System Simulation 116 3.1 Introduction 117 3.2 Multi-body Simulation Including Elastic Bodies 118 3.3 Methods of Model Order Reduction 120 3.4 Quality Assurance of the Model Order Reduction 124 3.5 Example for Model Order Reduction 128 3.6 Summary 133 References 134 Chapter 4 Identification of Temperature Dependent Material Properties in Composite Plates Utilizing Experimental Vibration Data 136 4.1 Introduction 136 4.2 Theory 139 4.2.1 Plate Theory 139 4.2.2 Numerical Methods 141 4.2.3 Operational Modal Analysis 142 4.2.4 Optimization Strategy 143 4.3 Measurements and Simulations 144 4.3.1 Measurement Setup 145 4.3.2 Test Sample 146 4.3.3 Numerical Model 147 4.4 Results 147 4.4.1 Experimental Results and Analysis 147 4.4.2 Identified Elastic Properties 148 4.5 Conclusion 151 4.6 Appendix 152 4.6.1 Mode Shapes of OMA 152 4.6.2 ANSYS Simulated Mode Shapes 153 References 154 Chapter 5 Unilateral Constraints and Multibody Dynamics 156 5.1 Introduction 156 5.2 Concepts of Dynamics 158 5.2.1 Bilateral Dynamics 158 5.2.2 Unilateral Dynamics 159 5.3 Impacts with Friction 164 5.3.1 General Theory 164 5.3.2 Energy Considerations 169 5.4 Contact Kinematics 172 5.4.1 Plane Contact Kinematics 173 5.4.2 Spatial Contact Kinematics 176 5.5 Numerical Aspects 180 5.6 Applications 181 5.6.1 Woodpecker, a Non-smooth Toy 182 5.6.2 Vibration Conveyor 187 5.6.3 Roller Coaster 189 5.6.4 Drop Tower Hydraulics 190 5.6.5 CVT Power Transmission 192 5.7 Conclusion 195 References 195 Chapter 6 Influence of Thermal Stabilisation on the Thermal Regime in the Strapdown Inertial Navigation System 198 6.1 Introduction 198 6.2 Description of the Model and Physical Process 200 6.3 Mathematical Framework and Solution Method 202 6.4 Results 203 6.5 Conclusions 207 References 208 Chapter 7 Experimental-numerical Analysis of Microstructure-property Linkages for Additively Manufactured Materials 210 7.1 Introduction 211 7.2 Methods 214 7.2.1 Experimental Characterisation of Microstructure and Defect Population 214 7.2.2 Numerical Characterisation of Microstructure and Defect Population, and Reconstruction 214 7.2.3 Microstructure Properties and Ranking 217 7.2.4 Grain Structure Characterisation 219 7.3 Results 221 7.3.1 Pore Microstructure-property Linkage 221 7.3.2 Grain Microstructure-property Linkage 222 7.4 Conclusions 225 References 226 Chapter 8 Multisurface Theory of Plasticity with one Active Surface: Basic Relations, Experimental Validation and Microstructural Motivation 228 8.1 Introduction 229 8.2 Conditions of Reversing 231 8.3 Constitutive Equations 232 8.4 Experimental Analysis 235 8.4.1 Test Results for Nickel Specimens 235 8.4.2 Test Results for Steel Specimens 241 8.5 Comparison of the Multisurface Model and the Microstructural Model Predictions 244 8.6 Numerical Implementation of the Constitutive Equations of the Multisurface Theory with one Active Surface 247 8.7 Finite-element Simulations 248 8.8 Conclusions 250 References 251 Chapter 9 A Damage Model for Corrosion Fatigue due to Hydrogen Embrittlement 254 9.1 Introduction 255 9.2 Model Description 256 9.2.1 Hydrogen Formation, Adsorption, and Absorption 257 9.2.2 Damage Analysis 260 9.3 Numerical Results and Discussions 262 9.3.1 Hydrogen Adsorption and Absorption 263 9.3.2 Parameters of Damage Model 265 9.3.3 Influences of Frequency on the Fatigue Life 268 9.3.4 Influences of Stress Ratio 269 9.4 Conclusions 272 9.5 Appendix 273 References 274 Chapter 10 A Thermodynamics-BasedWear Model and its Application with the Finite Element Analysis 276 10.1 Introduction 276 10.2 Wear Equation Based on a Thermodynamics Approach 278 10.3 Application with the Finite Element Analysis 281 10.3.1 Time Discretization 281 10.3.2 Contact Iteration 282 10.4 The Wear Simulation of Timing Chains 283 10.4.1 Experimental Investigations 283 10.4.2 Description of the Finite Element Model 285 10.4.3 Determining an Extrapolation Factor for the Wear Simulation 288 10.5 Summary 289 References 291 Chapter 11 Discrete Description of Crack Kinematics in Regularized Free Discontinuities of Crack Faces 292 11.1 Introduction 292 11.2 Representative Crack Elements 296 11.2.1 Structure and Notation 296 11.2.2 Kinematic Coupling 297 11.3 Regularization of the Free Discontinuity Problem 304 11.3.1 Governing Equations 304 11.3.2 Stress and Consistent Tangent 306 11.4 Numerical Applications 308 11.4.1 Self-consistent Test 308 11.4.2 A Single Edge Notch Plate (SENP) at Shear Load 314 11.4.3 Structural Fracture at Finite Strain 315 11.4.4 Cohesive Failure Modeling 320 11.4.5 Contact Friction Modeling 323 11.5 Conclusions 327 References 327 Chapter 12 Applications of Viscoplasticity and Damage Models, the Thermomechanical Consistency and the Prospect of a Microstructural Representation 332 12.1 Introduction 333 12.2 Experimental and Numerical Investigation of Temperature-dependent Mechanical Behaviour of 3D Printed Polyamide 12 334 12.2.1 Experimental Analysis 335 12.2.2 Microanalysis 336 12.2.3 Numerical Analysis 337 12.2.4 Results 343 12.3 Thermomechanical Approach 344 12.3.1 Analytical Formulation in the Framework of Continuum Thermomechanics 345 12.3.2 Experimental Approach 348 12.3.3 Results and Discussion 348 12.4 Numerical Models Based on CT Data 350 12.5 Summary 353 References 354