Topology-Based Modeling of Textile Structures and Their Joint Assemblies (eBook)

Dr Yordan Kyosev is Professor of textile materials, textile technology and quality management at the Faculty of Textile and Clothing Technology, Niederrhein University of Applied Sciences, Germany. He has extensive expertise in both braiding technology and mathematical modelling of braided products, and is the author of numerous publications on braiding, he is also the main developer of the leading braiding CAD software, Texmind Braider.                

Preface 5
Formal Remark 7
Acknowledgements 8
Contents 9
Introduction 14
1 Introduction and Problem Definition 15
1.1 Modelling of Textiles 15
1.2 Strategies for Multiscale Modelling of Textiles 17
1.3 Content of the Book 19
References 19
Braided Structures 22
2 Topology Based Models of Tubular and Flat Braided Structures 23
2.1 Introduction 23
2.2 State of the Art 23
2.3 3D Models of Braids with Floating Length of Two (Regular Braids) 26
2.4 Generalized Model for Yarn Path of Braid with Arbitrary Floating Length 28
2.5 Multiple Yarns in a Group 30
2.5.1 Where Is the Problem? 32
2.5.2 Topology Based Solution of the Mechanical Problem 33
2.5.3 Flat Braids with Multiple Yarns in a Group 36
2.6 Triaxial Briads 38
2.7 Configuration for Different than 45° Braiding Angle 41
2.8 Conclusions 44
References 44
3 Evaluation of the Properties of Braided Structures Based on Topological Models 46
3.1 Introduction 46
3.2 Relation Between the Braiding Angle and the Elongation of the Braided Products 46
3.3 Relation Between the Braiding Angle and the Braiding Diameter During Axial Deformation 49
3.4 Unit Cell Geometry 50
3.5 Yarn Compression and Jamming Limits 56
3.5.1 Notice on the Geometrical Models 59
3.6 Cover Factor for Biaxial Braids 60
3.7 Cover Factor for Triaxial Braids 62
3.8 Characteristic Points of the Force-Elongation Diagram 66
3.9 Yarn Length Per Unit Length of Braid 68
3.10 Weight Per Meter 71
3.11 Conclusions 71
References 71
4 Process Emulation Based Development of Braided Structures and Machines 73
4.1 Introduction 73
4.2 Task Definition 74
4.3 Virtual Machine Components 75
4.4 Track Based Model 79
4.4.1 Method 79
4.4.2 Automated Track Generation 82
4.4.3 Problems with Track Based Models 84
4.5 Horn Gear Based Model 85
4.6 Automated Carrier Arrangement 86
4.6.1 Motion Emulation and Build of Simplified Virtual Braid 88
4.7 Algorithm Implementation 90
4.8 Simulated Braids 90
4.9 Future Steps 93
4.10 Conclusions 94
References 94
Knitted Structures 96
5 Topological Modelling of Knitted Structures 97
5.1 Classification of Knitted Structures 97
5.2 Scales in the Structure 99
5.3 Structural Elements of Knitted Structures at Meso-scale 101
5.4 Topology Description 101
5.5 Loops and Loops Only Based Knitted Structures 103
5.5.1 Early Analytical Models for Geometry Relations of Knitted Loops 104
5.5.2 Analytical Model of Choi 105
5.5.3 Extended Analytical Model for Elliptical Yarn Cross Section 105
5.5.4 Topology Using List of Key Points 109
5.5.5 Software for Loop Based Structures on One or Two Needle Beds 112
5.6 Hold Loops and Tuck Loops 112
5.7 Plating Loops 113
5.7.1 Underlaps in Plated Loops 121
5.7.2 Transferred Loops 125
5.8 Plated Loops in Double Needle Bed Structures 125
5.9 Weft Insertion 126
5.10 Weft and Warp Yarns Reinforced Knitted Structure (MLG) 129
5.11 Other or Modified Structural Elements 133
5.12 Conclusions 133
References 134
6 Truss Framework Model for Warp Knitted Structures 136
6.1 Warp Knitted Structures as Truss Framework 136
6.2 Related Works 136
6.3 Theoretical Background of the FEM for Truss Based Frames 138
6.4 Implementation 141
6.5 Boundary Conditions 141
6.6 Implementation and Verification 142
6.7 Possible Extension for Double Needle Bed Structures 142
6.8 Limitations of the Method 146
6.8.1 Stiffness Matrix and Singularities 146
6.8.2 Model Limitations 149
6.8.3 Elasticity Module of the Trusses 150
6.9 Conclusions 152
References 152
Woven Structures and Sewing Stitches 153
7 Notes About Topological Methods for Woven Structures 154
7.1 Introduction 154
7.2 Single Layer Structures 154
7.3 Multiple Layer Structures 155
7.4 Irregular Pattern 156
7.5 Conclusions 158
References 159
8 Topology Based Modeling of Sewing Stitches 160
8.1 Introduction 160
8.2 State of the Art 160
8.3 Hand Stitch—Class 209 161
8.4 Lock Stitch—Class 301 163
8.5 Class 101 167
8.6 More Stitches 167
8.7 Conclusions 168
References 169
Multiscale Modelling—Assemblies, Filaments and Their Software Implementation 170
9 Extending to Filament Level and Interpolation Issues 171
9.1 Introduction 171
9.2 Yarn Cross Section Form 171
9.3 Cross Section Definition for Multifilament Modelling 173
9.4 Natural Curvature and Artificial Yarn Twist 175
9.5 Interpolation Issues 176
9.6 Too High Resolution at High Curvature Areas 178
9.7 Highly Different Curvatures 179
9.8 Interpolated Areas 179
9.9 Solution Strategies 180
9.10 Examples 181
9.11 Conclusions 183
References 183
10 Assembly Level—From Textile Structures to Textile Assemblies 185
10.1 Introduction 185
10.2 Structural Cells 185
10.3 Application for 3D Structures 188
10.3.1 Spacer Fabrics with Stepwise Different Thickness 188
10.3.2 Hollow Structures 190
10.4 Assembly Position and Orientation 191
10.5 Cutting of Fabrics 192
10.6 Stitching 194
10.7 Conclusion 195
References 196
11 Data Structures for Multiscale Modelling of Flexible Assemblies and Software 197
11.1 Software Implementation 197
11.2 Modelling Issue—Levels in Textile Structures 198
11.3 Software Overview—Comparative Analysis of the Available Packages 201
11.4 Conclusions 203
References 203
Mechanics After Topology—Application of Topological Based Models for Mechanical Simulations 205
12 Computational Mechanics of the One Dimensional Continuum as Refinement of the Topology Based Models 206
12.1 Introduction 206
12.2 Energy Minimisation 206
12.3 Force Equilibrium Approach 208
12.3.1 Continuous Model 209
12.3.2 Discretised Model 209
12.3.3 Dimensionless Discretized Model 211
12.3.4 Boundary Conditions 212
12.3.5 Numerical Integration 212
12.3.6 Numerical Results 213
12.4 Force Equilibrium Approach for Textile Structures 215
12.4.1 Damping 215
12.4.2 Bending 215
12.5 Contact Treatment 216
12.6 Friction 218
12.7 Conclusions 219
References 219
13 Applications of the Topological Generated Models 221
13.1 Introduction 221
13.2 Deformations of Weft Knitted Structures With LS-Dyna and Hyperworks 221
13.3 Truss and Beam Finite Elements 222
13.4 Digital Chain Method 224
13.5 Homogenisation for Composites 226
13.6 Further Possible Application Areas 230
13.7 Conclusions 230
References 231
Summary About the Topology Based Methods 233
Outlook 237