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 |  موضوع: كتاب Mechanical Response of Composites السبت 08 أغسطس 2020, 10:04 pm | |
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Mechanical Response of Composites
Pedro P. Camanho , C.G. Davila , S.T. Pinho , J.J.C. Remmers
و المحتوى كما يلي :
Contents
1 Computational Methods for Debonding in Composites 1
Ren´ e de Borst and Joris J.C. Remmers
1.1 Introduction 1
1.2 Levels of Observation 3
1.3 Zero-Thickness Interface Elements 5
1.4 Solid-Like Shell Formulation . 12
1.5 The Partition-of-Unity Concept 15
1.6 Delamination in a Solid-Like Shell Element . 21
1.7 Concluding Remarks 23
References . 24
2 Material and Failure Models for Textile Composites 27
Raimund Rolfes, Gerald Ernst, Matthias Vogler, and Christian H¨ uhne
2.1 Introduction 28
2.2 Multiscale Analysis . 29
2.2.1 Homogenization 31
2.2.2 Voxel Mesh 32
2.2.3 Micromechanical Unit Cell . 33
2.2.4 Mesomechanical Unit Cell 34
2.3 Material Models 37
2.3.1 Isotropic Elastic-Plastic Material Model
for Epoxy Resin . 37
2.3.2 Transversely Isotropic Elastic-Plastic Material Model
for Fiber Bundles . 44
2.3.3 Transversely Isotropic Damage Formulation . 50
2.4 Results of Micromechanical Unit Cell Computations 51
2.4.1 Comparison with Test Results from WWFE . 52
2.4.2 Results of Micromechanical Unit Cell
for Homogenization . 54
2.5 Conclusion . 55
References . 55
ixx Contents
3 Practical Challenges in Formulating Virtual Tests
for Structural Composites 57
Brian N. Cox, S. Mark Spearing, and Daniel R. Mumm
3.1 Introduction – The Concept of a Virtual Test . 58
3.2 The Structure of a Virtual Test – Formalizing
the Link Between Experiment and Theory . 60
3.3 The System Management Challenge . 62
3.4 Experiments That Guide Model Formulations 64
3.5 Challenges in Observing Mechanisms 68
3.6 The Cycle of Calibration and Validation 70
3.7 Concluding Remarks 72
References . 73
4 Analytical and Numerical Investigation of the Length
of the Cohesive Zone in Delaminated Composite Materials . 77
Albert Turon, Josep Costa, Pedro P. Camanho, and Pere Maim´?
4.1 Introduction 77
4.2 Length of the Cohesive Zone for Isotropic Materials 78
4.3 Length of the Cohesive Zone for Orthotropic Materials 80
4.3.1 Length of the Cohesive Zone Under Mixed–Mode
Loading . 82
4.4 Generalization of the Length of the Cohesive Zone
for Finite-Sized Geometries . 83
4.4.1 Mode II 85
4.4.2 Mixed-Mode I and II . 86
4.5 Validation of the Model 86
4.5.1 Numerical Model 86
4.5.2 Mode I loading . 88
4.5.3 Mode II Loading 90
4.5.4 Mixed-Mode Loading 91
4.6 Updated Engineering Solution to Use Coarse Meshes . 93
4.7 Conclusions 96
References . 96
5 Combining Elastic Brittle Damage with Plasticity to Model
the Non-linear Behavior of Fiber Reinforced Laminates . 99
Clara Schuecker and Heinz E. Pettermann
5.1 Introduction 100
5.2 Plasticity Model 102
5.2.1 Plastic Strain for ? f p = 0 (Puck Modes A and B) . 102
5.2.2 Plastic Strain for ? f p = 0 (Puck Mode C) . 103
5.2.3 Identification of Parameters for the Plasticity Model 104
5.2.4 Lamina Response for Mode C . 106
5.3 Combination with Damage Model . 108
5.4 Laminate Behavior 110
5.4.1 Influence of Curing Stresses on Shear Behavior 110Contents xi
5.4.2 Accumulation of Plastic Strain 111
5.5 Conclusions 115
References . 116
6 Study of Delamination in Composites by Using the Serial/Parallel
Mixing Theory and a Damage Formulation 119
Xavier Mart´?nez, Sergio Oller, and Ever Barbero
6.1 Introduction 120
6.2 Formulation 121
6.2.1 Serial/Parallel Mixing Theory . 121
6.2.2 Tangent Constitutive Tensor . 124
6.2.3 Isotropic Continuum Damage Formulation 126
6.3 End Notch Flexure (ENF) Test Simulation 131
6.3.1 Experimental Test Description . 131
6.3.2 Numerical Model Description . 132
6.3.3 Comparison Between the Numerical
and the Experimental Results 133
6.3.4 Detailed Study of the Numerical Results 135
6.4 Conclusions 138
References . 139
7 Interaction Between Intraply and Interply Failure in Laminates 141
F.P. van der Meer and L.J. Sluys
7.1 Introduction 141
7.2 Softening Orthotropic Plasticity . 142
7.2.1 Viscoplastic Regularization . 144
7.2.2 Stress Evaluation 145
7.2.3 Consistent Linearization 149
7.2.4 Convergence Issue . 151
7.2.5 Associativity Versus Non-associativity 152
7.3 Delamination . 154
7.4 Numerical Example . 156
7.5 Discussion . 158
References . 159
8 A Numerical Material Model for Predicting the High Velocity
Impact Behaviour of Polymer Composites . 161
Lucio Raimondo, Lorenzo Iannucci, Paul Robinson,
and Silvestre T. Pinho
8.1 Introduction 161
8.2 A Phenomenological Model for Predicting
Material Non-linear Effects in UD Plies
Under Compressive/Shear Loading Conditions . 162
8.2.1 Premise 162
8.2.2 Outline of the Modelling Approach . 162
8.2.3 Shear Non-linear Stress-Strain Behaviour . 163xii Contents
8.2.4 Modelling Effects of Mechanical (or “Internal”)
Friction on Progressive Failure Development 164
8.2.5 Modelling Progressive Failure in Matrix Dominated
Modes . 166
8.2.6 Validation of the 3D Plasticity Model . 167
8.3 Modelling Strain Rate Effects in Compression . 168
8.3.1 Premise and Outline Modelling Approach . 168
8.3.2 Shear Strain Rate Dependent Behaviour . 168
8.3.3 Modelling Strain Rate Effects in Matrix Dominated
Modes of Deformation . 169
8.3.4 Validation of the 3D Strain-Rate Dependent Plasticity
Model . 169
8.4 Strain-Rate Dependent Energy-Based Damage Mechanics
Approach 170
8.5 Validation of the Impact Damage Model 174
8.6 Conclusions 175
References . 177
9 Progressive Damage Modeling of Composite Materials
Under Both Tensile and Compressive Loading Regimes . 179
N. Zobeiry, A. Forghani, C. McGregor, R. Vaziri, and A. Poursartip
9.1 Introduction 179
9.2 Description of the CODAM Model . 183
9.3 Model Calibration . 185
9.4 Model Validation . 188
9.4.1 Simulation of OCT Test 188
9.4.2 Simulation of Open Hole Plates Under Compression 189
9.5 Non-local Approach . 190
9.5.1 Limitations of Local Damage Models . 190
9.5.2 Non-local Regularization . 191
9.6 Conclusions 193
References . 194
10 Elastoplastic Modeling of Multi-phase Metal Matrix Composite
with Void Growth Using the Transformation Field Analysis
and Governing Parameter Method . 197
Ernest T.Y. Ng and Afzal Suleman
10.1 Introduction 197
10.2 Micromechanics 199
10.2.1 Setting the Stage 199
10.2.2 Governing TFA Equations 200
10.3 GPM Algorithm 202
10.4 Gurson-Tvergaard Model in GPM . 203
10.4.1 Gurson-Tvergaard Yield Criterion 203
10.4.2 Newton’s Method . 205
10.4.3 Ranges of ?eP m and ?e¯P 206Contents xiii
10.5 Verifications and Examples . 210
10.5.1 Test Cases 210
10.5.2 Discussion on the Evaluation Process . 215
10.5.3 4-phase Composite Material . 216
10.6 Closing Remarks 219
Appendix – The four partial derivatives . 219
References . 220
11 Prediction of Mechanical Properties of Composite Materials
by Asymptotic Expansion Homogenisation 223
J.A. Oliveira, J. Pinho-da-Cruz, and F. Teixeira-Dias
11.1 Introduction 224
11.2 Asymptotic Expansion Homogenisation 224
11.2.1 AEH in Linear Elasticity . 224
11.2.2 Localisation Methodology 228
11.3 Finite Element Method in AEH 229
11.3.1 Corrector ? 229
11.3.2 Periodicity Boundary Conditions 229
11.3.3 Homogenised Elasticity Matrix Dh . 230
11.4 Numerical Procedures . 230
11.4.1 The Main Program 230
11.4.2 Representative Unit-Cell Generation 231
11.4.3 Automatic Association of Degrees of Freedom . 231
11.5 Numerical Applications 233
11.6 Final Remarks 240
References . 241
12 On Buckling Optimization of a Wind Turbine Blade 243
Erik Lund and Leon S. Johansen
12.1 Introduction 243
12.2 Discrete Material Optimization (DMO) Approach 245
12.2.1 Parametrization for Single Layered Laminate Structures . 246
12.2.2 Parametrization for Multi Layered Laminate Structures 247
12.2.3 Patch Design Variables . 247
12.2.4 DMO Convergence 247
12.3 Analysis and Design Sensitivity Analysis . 248
12.4 The Optimization Problem 249
12.5 Buckling Optimization of Wind Turbine Blade Test Section 250
12.6 Conclusion . 258
References . 258
13 Computation of Effective Stiffness Properties for Textile-Reinforced
Composites Using X-FEM 261
M. K¨ astner, G. Haasemann, J. Brummund, and V. Ulbricht
13.1 Homogenization 261
13.1.1 Boundary Conditions and Deformation Modes . 264xiv Contents
13.1.2 Effective Properties 268
13.1.3 Summary 269
13.2 Application of the eXtended Finite Element Method (X-FEM)
to Modelling of Textile-Reinforced Composites 269
13.2.1 Fundamentals . 270
13.2.2 Definition of X-elements . 271
13.2.3 Automated Model Generation . 274
13.3 Effective Material Properties of GF-PP Woven Fabric . 275
13.3.1 Effective Yarn Properties . 275
13.3.2 Effective Properties of Plain Weave Fabric . 276
13.3.3 Experimental Verification . 278
13.4 Conclusion . 278
References . 279
14 Development of Domain Superposition Technique for the Modelling
of Woven Fabric Composites 281
Wen-Guang Jiang, Stephen R. Hallett, and Michael R. Wisnom
14.1 Introduction 281
14.2 Domain Superposition Technique 282
14.2.1 Coupling Technique . 283
14.2.2 Material Models 284
14.3 Numerical Analysis Results . 285
14.3.1 Convergence Study of DST . 286
14.3.2 Comparison Between DST and Conventional
FE Analysis 289
14.4 Conclusions 290
References . 290
15 Numerical Simulation of Fiber Orientation and Resulting
Thermo-Elastic Behavior in Reinforced Thermo-Plastics 293
H. Miled, L. Silva, J.F. Agassant, and T. Coupez
15.1 Introduction 293
15.2 Modelling Flow-Induced Fiber Orientation 295
15.2.1 Evolution Equation of Fiber Orientation . 295
15.2.2 Numerical Resolution of Folgar and Tucker’s Equation 297
15.2.3 Validation on an Industrial Part 299
15.3 Predicting Thermo-Elastic Properties of the Composite 302
15.3.1 Unidirectional Properties . 303
15.3.2 Anisotropic Properties . 305
15.4 Results and Discussion . 306
15.4.1 Choice of a Micromechanical Model
for the Unidirectional Properties . 306
15.4.2 Effective Properties of a Three-Dimensional Plate 308
15.5 Conclusion . 310
References . 311
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