Computational Modeling, Optimization and Manufacturing Simulation of Advanced Engineering Materials (eBook)

Pablo Andrés Muñoz-Rojas (Herausgeber)

eBook Download: PDF

2016 | 1st ed. 2016
VIII, 393 Seiten
Springer International Publishing (Verlag)
978-3-319-04265-7 (ISBN)

Infos

This volume presents recent research work focused in the development of adequate theoretical and numerical formulations to describe the behavior of advanced engineering materials. Particular emphasis is devoted to applications in the fields of biological tissues, phase changing and porous materials, polymers and to micro/nano scale modeling. Sensitivity analysis, gradient and non-gradient based optimization procedures are involved in many of the chapters, aiming at the solution of constitutive inverse problems and parameter identification. All these relevant topics are exposed by experienced international and inter institutional research teams resulting in a high level compilation. The book is a valuable research reference for scientists, senior undergraduate and graduate students, as well as for engineers acting in the area of computational material modeling.

Inhalt

Preface 6
Contents 8
Micro and Nanoscale Modeling 10
On the Variational Analysis of Vibrations of Prestressed Six-Parameter Shells 11
1 Introduction 11
2 Dynamics and Statics of Micropolar Plates and Shells 13
3 Linearized Boundary-Value Problems 17
4 Eigen-Vibrations of Prestressed Micropolar Shells 20
5 Rayleigh Principle 20
6 Conclusions 24
References 24
Multi-objective Topology Optimization Design of Micro-structures 28
1 Introduction 28
2 Multi-objective Problem Formulation 29
2.1 Preliminaries in the Multi-scale Modeling 30
2.2 The Homogenized Conductivity Tensor 31
2.3 The Homogenized Elasticity Tensor 34
3 Topological Derivative 37
4 Numerical Results 42
4.1 Example 1. Bulk Modulus and Horizontal Conductivity Maximization 45
4.2 Example 2. Bulk Modulus and Orthogonal Conductivity Maximization 46
4.3 Example 3. Poisson's Ratio and Horizontal Conductivity Maximization 47
4.4 Example 4. Poisson's Ratio Minimization and Horizontal Conductivity Maximization 48
4.5 Example 5. Poisson Ratio Minimization and Orthogonal Conductivity Maximization 49
4.6 Example 6. Shear Modulus and Horizontal Conductivity Maximization 51
5 Concluding Remarks 52
References 52
3 Sensitivity Analysis of Micro Models for Solidification of Pure Metals 55
Abstract 55
1 Introduction 55
2 Governing Equations 57
3 Nucleation and Nuclei Growth 60
4 Sensitivity Analysis 65
5 Final Remarks 69
Acknowledgments 69
References 69
Biological Tissues 71
Variational Constituive Models for Soft Biological Tissues 72
1 Background 72
2 Variational Framework 73
3 A Set of Variational Inelastic Models 76
3.1 A Viscoelastic Model for Isotropic Soft Materials 77
3.2 A Viscoelastic Model for Fiber-Reinforced Soft Materials 79
3.3 A Viscoplastic Model for Isotropic Soft Materials Undergoing Permanent Deformations 82
3.4 Material Models 84
3.5 Tangent Moduli 86
4 Numerical Examples 87
4.1 Isotropic Viscoelastic Case 88
4.2 Viscoelastic Fiber-Reinforced Case 88
4.3 Elasto-Vicoplastic Model 90
5 Concluding Remarks 92
References 92
5 Sensitivity Analysis of Temperature Field and Parameter Identification in Burned and Healthy Skin Tissue 94
Abstract 94
1 Introduction 95
2 Governing Equations 96
3 Sensitivity Analysis 97
4 Boundary Element Method 99
5 Inverse Problem 107
6 Shape Sensitivity Analysis 108
7 Results of Computations 109
8 Conclusions 116
Acknowledgements 116
References 116
Application of the hp-FEM for Hyperelastic Problems with Isotropic Damage 118
1 Introduction 118
2 Hyperelasticity 120
2.1 Compressible Neo-Hookean Material 120
2.2 Nearly-Incompressible Mooney-Rivlin Material 121
2.3 Principle of Virtual Power (PVP) 123
2.4 Linearization of the Weak Form 124
2.5 High-Order Shape Functions 127
2.6 Local Finite Element Discretization 128
2.7 Local Pressure Projection 128
2.8 Discretization of the Equilibrium Equation 132
2.9 Discretization of the Linearized Equilibrium Equation 133
2.10 Global Newton-Raphson Equation 134
3 Hyperelastic Damage 135
3.1 Mullins Effect in Hyperelastic Materials 135
3.2 Damage Variable and Thermodynamic Aspects 136
3.3 Damage Criterion 138
3.4 Damage Evolution Law 139
3.5 Constitutive Relations 140
3.6 Damage Algorithm 141
4 Convergence Tests 143
4.1 Test 1---Nearly-Incompressible Mooney-Rivlin Material 144
4.2 Test 2---Damaged Neo-Hookean Material 149
4.3 Test 3---Damaged Nearly-Incompressible Mooney-Rivlin Material 150
5 Conclusion 153
References 154
Mechanical Characterization of the Human Aorta: Experiments, Modeling and Simulation 156
1 Introduction 157
2 Materials and Methods 161
2.1 Experimental Procedure 161
2.2 Constitutive Modeling 170
2.3 Material Characterization via the Tensile Test 172
2.4 Analysis of the Pressurization Test 174
3 Results 175
3.1 Ascending Aorta 175
3.2 Aortic Arch 178
3.3 Descending Aorta 186
4 Discussion 191
4.1 Ascending Aorta 191
4.2 Aortic Arch 195
4.3 Descending Aorta 199
5 Conclusions 200
6 Conflicts of Interest 202
References 203
Porous and Multiphase Materials 208
8 Optimization of Functionally Graded Materials Considering Dynamical Analysis 209
Abstract 209
1 Introduction 210
2 Functionally Graded Materials 211
3 Topology Optimization Method for FGM Design 214
3.1 Basics of the Topology Optimization Method 214
3.2 Topology Optimization of FGMs 218
4 Topology Optimization of Dynamically Loaded Structures 220
4.1 Dynamic Finite Element Analysis 220
4.2 Topology Optimized Structures Under Impact Loads 224
4.3 Equivalent Static Loads 226
4.4 The Optimization Process with ESLs 226
5 TOM-Based Design of FGMs Under Impact Loads 228
5.1 Heuristic Approach 228
5.2 Optimized Approach 233
6 Conclusions of the Chapter 240
Acknowledgments 240
References 240
Complex Variable Semianalytical Method for Sensitivity Evaluation in Nonlinear Path Dependent Problems: Applications to Periodic Truss Materials 242
1 Introduction 242
2 Nonlinear Truss Finite Element Formulation 244
2.1 Virtual Work 246
2.2 Internal Force Vector 247
2.3 Tangent Stiffness Matrix 248
2.4 Geometric Nonlinearity 249
2.5 Material Nonlinearity: A Coupled Elastoplastic Model for Ductile Damage 250
2.6 Tangent Modulus 255
3 Sensitivity Analysis 255
3.1 Sensitivity Analysis for Path Independent Problems 256
3.2 Sensitivity Analysis for Path Dependent Problems 260
4 Periodic Truss Material 264
4.1 Sensitivity Analysis of Periodic Truss Materials 264
4.2 Bulk Modulus Sensitivity Expression 267
4.3 Numerical Evaluation of the Bulk Modulus Sensitivity 268
5 Conclusion 270
References 271
10 Laser Beam Drilling of Cellular Metals: Numerical Simulation 274
Abstract 274
1 Introduction 275
2 Fundamentals of Laser Technology 276
2.1 Laser Beam Drilling Technology 276
2.2 Laser Beam Behavior 276
2.3 Homogenization and RVE 281
3 Program Code 283
3.1 Flow Chart of the Program Code 283
3.2 Finite Volume Method 284
4 Results 286
4.1 Sintered and Soldered Cells 288
4.2 Thermal Conductivity Influence 289
4.3 Considerations About the Results 293
5 Gradient of Temperature and Velocity of Drilling 294
6 Total Heat and Expected Heat 295
7 Drilling Width 296
8 Conclusions 298
References 299
11 Metallic Foam Density Distribution Optimization Using Genetic Algorithms and Voronoi Tessellation 301
Abstract 301
1 Introduction 302
2 Modeling of Open-Cell Foam Structures 303
3 Optimization 305
3.1 Density Modification of Foam 305
3.2 Genetic Algorithms 306
3.2.1 Selection 307
3.2.2 Crossover 307
3.2.3 Mutation 308
3.3 Fitness Function Evaluation 308
3.4 Algorithm 310
4 Applications 311
4.1 Example 1 311
4.2 Example 2 314
4.3 Example 3 316
5 Conclusions 317
Acknowledgments 318
References 318
Polymers 320
12 Modeling Material Behavior of Polymers 321
Abstract 321
1 Introduction 321
1.1 Micromolecular Background to Viscous and Solid Behavior 322
1.2 Types of Polymers and Their Tensile and Compressive Behavior 323
1.3 Experimental Considerations 327
1.4 Polymer Material Testing at the University of Waterloo 328
2 Constitutive Modeling 332
2.1 Micro- and Macro-Scale Modeling 332
2.2 Viscoelastic Modeling 333
2.3 Viscoplastic Modeling 335
3 Parameter Estimation for Linear Modeling 336
4 Nonlinear Modeling 339
4.1 Methods for ‘Nonlinearization’ of the Model Parameters 340
5 Extending the Material Parameters to Longer Times Frames 343
5.1 Using Short Term Testing for Predictions at Longer Time Frames 343
5.2 Viscoelastic (NVE) and Viscoplastic (NVP) Long Term Responses 344
6 Modeling the Response Under Varying Stress 346
6.1 Modified Superposition Principle (MSP) 346
7 Conclusion 349
References 350
Material Model Based on Response Surfaces of NURBS Applied to Isotropic and Orthotropic Materials 353
1 Introduction 354
2 Nonuniform Rational B-Spline Curves and Surfaces 355
2.1 Tensor Product Surfaces 355
2.2 Definition of B--Spline Basis Functions 356
2.3 Definition of B--Spline Curves 356
2.4 Definition of B--Spline Surfaces 357
2.5 Definition of NURBS Surfaces 359
2.6 Derivatives of a NURBS Surface 359
3 Data Fitting 361
4 Material Model Based on NURBS for Principal Directions (NURBS--Material) 362
5 Application of NURBS--Material in Membrane Finite Element Modeling 366
5.1 Comparison with Elastoplastic Material Model 366
5.2 Comparison with an Orthotropic Material Model 370
6 Conclusions 372
References 373
14 Characterization of Constitutive Parameters for Hyperelastic Models Considering the Baker-Ericksen Inequalities 374
Abstract 374
1 Introduction 374
2 Constitutive Parameters Optimization Technique 376
3 Imposing the Inequalities to the Models 380
4 Experimental Data 383
5 Results 384
6 Conclusions 390
References 391

Produkt-Details

• Erscheint lt. Verlag: 20.6.2016
• Reihe/Serie: Advanced Structured Materials
• Reihe/Serie: Advanced Structured Materials
• Zusatzinfo: VIII, 393 p. 215 illus., 87 illus. in color.
• Verlagsort: Cham
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Informatik
• Themenwelt: Mathematik / Informatik ► Mathematik ► Wahrscheinlichkeit / Kombinatorik
• Themenwelt: Technik ► Maschinenbau
• Schlagworte: Biological Tissue Modeling • Constitutive Models • Functionally Graded Materials • Inverse Problems • multiscale modeling • Polymer Behavior • Sensitivity Analysis
• ISBN-10: 3-319-04265-3 / 3319042653
• ISBN-13: 978-3-319-04265-7 / 9783319042657