Advances in Mechanics of Materials and Structural Analysis (eBook)

Preface 6
Contents 10
On Constitutive Models for the Momentum Transfer to Particles in Fluid-Dominated Two-Phase Flows 12
1 Introduction 13
2 Particle-Fluid Interaction in Fluid Dominated Flows 13
2.1 Viscous Fluid Flow 14
2.2 Particle Dynamics 15
2.3 Momentum Transfer in Particle-Fluid Interaction 15
3 Validation - Particle Transport in Couette and Lid-Driven Cavity Flows 24
3.1 Simulation Setup 25
3.2 Couette Flow 27
3.3 Lid-Driven Cavity Flow 30
4 Conclusions 34
References 35
Flexible Beam-Like Structures - Experimental Investigation and Modeling of Cables 37
1 Introduction 37
2 Experiments for Flexible Beam-Like Structures 38
2.1 Uniaxial Tensile Tests 38
2.2 Torsion Experiments 39
2.3 Bending Experiments 40
2.4 Discussion of Experiments 44
3 Modeling of Flexible Beam-Like Structures for Virtual Product Development 46
3.1 Kinematics of Geometrically Exact Rods 46
3.2 Deformation Measures 47
3.3 Static Equilibrium Equations 47
3.4 Constitutive Laws 48
4 Conclusions 54
References 55
On Phase Transformation Induced Effects Controlling the Flow Behavior of Ferritic-Martensitic Dual-Phase Steels 57
1 Introduction 57
2 Phase Transformation-Induced Stresses and Strains 60
3 Phase Transformation-Induced Macro-Scale Effects 63
4 Microscopic Effects of Macro-Deformation 65
5 Conclusions 67
References 68
Hygro- and Thermo-Mechanical Modeling of Wood at Large Deformations: Application to Densification and Forming of Wooden Structures 69
1 Introduction 69
2 Hygro- and Thermo-Mechanical Fundamentals of Wood 71
2.1 Kinematics at Finite Deformations, Temperature and Moisture Content 71
2.2 Stress Measures, Thermal and Hygric Quantities 74
2.3 Hygro-Thermo-Mechanical Equilibrium Conditions 74
3 Hygro- and Thermo-Mechanical Finite Element Formulations 77
3.1 Quasi-static Equilibrium 78
3.2 Thermal Equilibrium 79
3.3 Hygric Equilibrium 80
4 Constitutive Formulations 81
4.1 Helmholtz Free Energy, Cauchy Stresses and Hardening Response 81
4.2 Temperature and Moisture Dependent Constitutive Properties 89
5 Model Verification at Constant Moisture Content and Under Isothermal Conditions 90
5.1 Mechanical Modeling of Spruce Wood (Picea Abies) 90
5.2 Mechanical Modeling of Balsa Wood (Ochroma Pyramidale) 91
6 Model Validation at Heating of a Beech Wood (Fagus Sylvatica) Board 95
7 Modeling of Wood Densification and Forming Processes 98
7.1 Densification of a Beech Wood (Fagus Sylvatica) Board 99
7.2 Molding of Densified Beech Wood (Fagus Sylvatica) 99
8 Conclusions and Outlook 101
References 105
Damage and Fracture of Ductile Sheet Metals: Experiments and Numerical Simulations with New Biaxial Specimens 108
1 Introduction 108
2 Continuum Damage Model 111
3 Geometry 113
4 Numerical-Experimental Approach 114
5 Experimental and Numerical Results 117
6 Conclusion 123
References 124
Influence of Shear Correction Factors on Eigenfrequencies of Layered Plates 126
1 Introduction 126
2 Variational Formulation 127
2.1 Kinematics 127
2.2 Constitutive Equations for the Stress Resultants 129
2.3 Equilibrium Equations and a Constraint 130
2.4 Constrained Optimization Problem 132
3 Representative Volume Element 133
4 Examples 136
4.1 Comparison of Shear Correction Factors with Literature Results 136
4.2 Influence of Shear Correction Factors on Eigenfrequencies 138
5 Conclusions 140
References 141
Verification Examples for Strain and Strain-Rate Determination of Digital Image Correlation Systems 143
1 Introduction 143
2 Kinematics of Surfaces 145
2.1 Geometrical Description of Surfaces 146
2.2 Definition of Deformation 148
2.3 Strain Measures 152
2.4 Strains in Arbitrary Directions and Shear Angles 154
2.5 Thickness Strain Determination 155
3 Classical Strain Determination 156
3.1 Polynomial Description of Surfaces 159
3.2 Strain-Rate Calculation 161
4 Verification Examples 162
4.1 Simple Shear 163
4.2 Combined Tension and Torsion 166
4.3 Bending 169
4.4 Deep Drawing 171
5 Conclusions 177
6 Projection to Tangential Plane 178
7 Shape Functions 178
References 180
Closed-Form Approximate Solutions for the Local Buckling Behavior of Composite Laminated Beams Based on Third-Order Shear Deformation Theory 183
1 Introduction 183
2 Third Order Shear Deformation Theory 186
3 Structural Situation and Energy Formulation for Buckling Analysis 193
4 Governing Equations and Boundary Conditions 196
5 Closed-Form Approximate Solution 198
6 Shape Functions 201
7 Results and Discussion 203
8 Summary and Conclusions 210
References 212
Dislocation Dynamics as Gradient Descent in a Space of Currents 214
1 Introduction 214
2 Mathematical Preliminaries 215
3 Variational Methods and the Lie-Derivative of Currents 221
4 Energetics of Dislocation 222
5 Variational Calculus Applied to Dislocation Energies 223
6 Summary and Outlook 227
References 228
Optimum Design of Thick Laminated Anisotropic Plates via Frequency Regulation. A BEM Approach 229
1 Introduction 229
2 Statement of the Problem 231
2.1 Optimization Problem 231
2.2 The Equation of Motion of a Thick Laminated Anisotropic Plate 231
2.3 Evaluation of the Objective Function 234
2.4 The Optimization Procedure 236
3 Examples 237
4 Conclusions 244
References 244
Application of Piezoelements in a Structured Thin-Walled Shaft Material to Active Control of Stability and Vibration 246
1 Introduction 247
2 Piezoelectric Beam Transducer with Shunting Circuit 248
3 Dynamics of Beck's Column with Shunted Piezotransducer 249
4 Torsional Resonance of a Shaft with Shunted Piezotransducer 252
5 Active Damping of Torsional Vibration in Shafts Made of Piezoelectric Composites 255
6 Conclusions 262
References 264
Remarks on a Fluid-Structure Interaction Scheme Based on the Least-Squares Finite Element Method at Small Strains 266
1 Introduction to Fluid-Structure Interaction 266
2 The Least-Squares Finite Element Method 268
3 A Least-Squares Finite Element Based Fluid-Structure Interaction Scheme 270
3.1 Governing Equations for the FSI Scheme 270
3.2 Least-Squares Finite Element Formulation for the Fluid Part 271
3.3 Least-Squares Finite Element Formulation for the Solid Part 273
3.4 Finite Element Discretization in Space 275
4 Numerical Example 276
5 Conclusion 278
References 282
Dynamic Analysis of Gradient Poroelastic Solids and Structures 285
1 Introduction 285
1.1 Governing Equations of Motion 286
1.2 Wave Propagation Analysis 288
1.3 The Dynamic Gradient Poroelastic Column Problem 294
2 Conclusions and Recommendations for Future Research 298
References 299
Microstructured Multiferroic Materials: Modelling Approaches Towards Efficiency and Durability 301
1 Introduction 301
2 Constitutive Behaviors: Compilation of Equations 303
3 Constitutive Models for Ferromagnetic Materials 305
3.1 Physically Motivated Ferromagnetic Model 305
3.2 Phenomenological Ferromagnetic Model 308
4 Condensed Method: Application to Multiferroic Compounds 312
5 Continuum Damage Model 315
6 Results 319
6.1 Ferroelectric, Ferromagnetic and Multiferroic Behavior from FE Simulation 319
6.2 Constitutive Behavior and ME Coupling Predicted from the Condensed Method 325
7 Conclusion 328
References 330
Biaxial Tensile Tests and Microstructure-Based Inverse Parameter Identification of Inhomogeneous SMC Composites 333
1 Introduction 333
2 Experimental Procedure 335
3 Inverse Parameter Identification 337
3.1 Note on Fiber Orientation Tensors 338
3.2 Implications by the Assumption of the Linearity Between the Stiffness Tensor and the Fiber Orientation Tensor 340
3.3 Numerical Treatment of the Optimization 340
4 Results and Discussion 342
5 Conclusions 345
References 345
Configurational Forces in a Phase Field Model for Dynamic Brittle Fracture 347
1 Introduction 347
2 A Phase Field Model for Dynamic Brittle Fracture 348
3 Configurational Force Balance for a Phase Field Model for Dynamic Brittle Fracture 352
4 Discussion of the Configurational Force Balance 355
5 Numerical Examples 359
5.1 Crack Arrest 360
5.2 Branching 363
6 Conclusions 366
References 367
A Multi-layer Piezocomposite Model and Application on Controlled Smart Structures 369
1 Introduction 370
2 Governing Equations 372
2.1 Mechanical Displacement and Strains 372
2.2 Constitutive Equations of Piezoelectric Lamina 373
2.3 Electric Field 374
2.4 Finite Element Formulation 374
2.5 Variational Principle 376
2.6 Equations of Motion 379
2.7 Modal Model in Terms of State Space 380
2.8 Control Law 381
3 Numerical Applications 382
3.1 Validation Example 1 382
3.2 Validation Example 2 383
3.3 Shape Control Applications 384
3.4 Vibration Control Applications 386
4 Conclusion 388
References 388
Optimal Design of Disks Under Large Creep Deformation 390
1 Introduction 390
2 Optimal Design of Full Disks with Respect to Mixed Creep Rupture Time 392
2.1 Mathematical Model of Disk with Respect to the Mixed Creep Rupture Time 392
2.2 Numerical Solutions 397
2.3 Optimal Solutions 402
3 Optimal Design of Annular Disks with Respect to Mixed Creep Rupture Time 408
3.1 Mathematical Model of Annular Disk with Respect the Mixed Creep Rupture Time 408
3.2 Influence of Boundary Conditions 410
4 Conclusions 417
References 418
A J-Interaction Integral to Compute Force Stress and Couple Stress Intensity Factors for Cracks in Functionally Graded Micropolar Materials 421
1 Introduction 422
2 Fracture Mechanics of FGMMs 423
2.1 Governing Equations for Micropolar Elasticity 423
2.2 Crack-Tip Asymptotic Fields in FGMMs 424
3 Interaction Integral (I-integral) 428
3.1 Three Formulations of the Auxiliary Field 429
3.2 Numerical Calculation of the I-Integral 430
3.3 Extraction of the FSIFs and CSIFs 432
4 Patched XFEM for Micropolar Materials 433
5 Numerical Examples 435
5.1 Internal Cracks 435
5.2 Edge Cracks 439
6 Summary and Conclusions 447
References 448
Analytical Modelling of the Tooth Translational Motions: Comparative Analysis for Different Shapes of Root 451
1 Introduction 452
2 Methods 453
2.1 Modelling of the Tooth Root Equilibrium in the PDL 453
2.2 Hydrostatic Stresses 454
3 Results 454
3.1 Hydrostatic Stresses Pattern 455
3.2 FE Modelling 457
4 Conclusions 459
References 462