IUTAM Symposium on Scaling in Solid Mechanics (eBook)

Preface 5
Contents 7
Contributors 10
Universal Effective Toughness Distribution for Heterogeneous Brittle Materials 14
1 Introduction 14
2 Crack Depinning as a Critical Phenomenon 15
3 Analysis of Indentation Data 19
4 Conclusions 21
References 22
Scaling Transformations in Solid Mechanics 24
1 Introduction 24
2 Similarity, Dimensional Analysis and Homogeneity 26
3 Non-Classical Scalings 30
4 Conclusion 37
References 37
Mathematical Foundations of Non-Classical Extensions of Similarity Theory 40
1 Introduction 40
2 Non-Classical Extensions 42
3 Summary 46
4 Conclusion 47
References 47
Perturbing Paths of Slow Cracks in PMMA by Local Heating 49
1 Introduction 49
2 Experimental Procedures 50
3 Quasi-Static Cracks Under Tensile Loading 53
4 Redirection of Quasi-Static Cracks Using Secondary Loading 56
5 Discussion 58
References 59
Multiscale Hybrid Materials with Negative Poisson’s Ratio 60
1 Introduction 60
2 Negative Poisson’s Ratio in Granulate Materials 62
3 Negative Poisson’s Ratio of Material with Multiscale Distribution of Non-Sliding Cracks 64
4 Hybrid Material with Multiscale Distribution of Negative Poisson’s Ratio Inclusions 66
5 Conclusions 67
References 68
Modelling of Size Effects with Gradient-Enriched Continuum Theories 70
1 Introduction 70
2 Gradient Theories 71
3 Strain Concentrations in the Elastic Field 72
4 Peak Loads of Notched and Unnotched Beams 74
5 Energy Dissipation in Elementary Volumes 76
6 Conclusions 78
References 79
Internal Variables and Scale Separation in Dynamics of Microstructured Solids 80
1 Introduction 80
2 Local Balance Laws 81
3 Canonical Thermomechanics on the Material Manifold 82
4 Internal Variables 84
5 Scale Separation 86
6 Example: Microstructure in One-Dimension 87
7 Conclusions 90
References 90
On Rational Boundary Conditions for Higher-Order Long-Wave Models 92
1 Introduction 92
2 Governing Equations 93
3 Essential Boundary Conditions 96
4 Concluding Remarks 100
References 100
Scaling of Physical Processes in Fluid-Driven Fracture: Perspective from the Tip 102
1 Introduction 102
2 The Tip Boundary Layer Problem 103
3 Scaling of Non-Dominant Processes in the Global Fracture Solution 106
References 110
Space and Time Scaling Laws Induced by the Multiscale Fracturing of The Arctic Sea Ice Cover 112
1 Introduction 112
2 Scaling of Sea Ice Dispersion and Deformation 113
3 A Multiscale Statistical Model of Sea Ice Fracturing and Deformation 114
4 The Contribution of Small vs Large Events to Global Sea Ice Deformation 118
5 Conclusion 119
References 119
Similarity Approach to Hertz Type Contact Problems 121
1 Introduction 121
2 The Classic Elastic Contact Problems 122
3 Contact Problem Between a Punch and an Incompressible Isotropic Plastic (Nonlinearly Elastic) Half-Space 125
4 Contact Problems in the Case of Linear Creep of Materials 126
5 Generalizations of Similarity Methods in Hertz Type Contact 127
6 Self-Similar Problems of Elastic Contact for Non-Convex Punches 128
7 Some Engineering Applications 129
8 Conclusion 130
References 131
Multiscale Modelling in Contact Mechanics 133
1 Introduction 133
2 Two-Scales Analysis in Normal Contact of Elastic Bodies with Rough Surfaces 134
3 Multiscale Approach toWear Modeling 137
4 Conclusions 143
References 143
Recent Progress in Energetic Probablistic Scaling Laws for Quasi-Brittle Fracture 145
1 Introduction 145
2 Conspectus of Main Results 146
3 Review of Size Effect in Weakest Link Model and Its Asymptotics 149
4 Size Effect on Mean Strength via Asymptotic Matching 150
5 Grafted Weibull-Gaussian Strength Distribution for any Size 151
6 Size Effect on Structure Lifetime 152
7 Closing Comments 154
References 154
The Fractal-Statistical Nature of Size-Scale Effects on Material Strength and Toughness 155
1 Introduction 155
2 Size Scale-Effect on the Tensile Strength of Bodies Containing Many Imperfections 156
3 Size-Scale Effect on Fracture Energy of Grained Materials 158
4 The Case of Imperfect Similarity 160
5 On the Upper Cut-Off of the Maximum Defect (or Grain) Size 161
6 Monte Carlo Numerical Simulations 162
7 Conclusions 163
References 164
Scaling Laws for Properties of Materials with Imperfect Interfaces 166
1 Introduction 166
2 Scaling Laws for Elastic Properties 167
3 Scaling Laws for Conductivities 169
4 Conclusions 171
References 171
Burst Statistics as a Criterion for Imminent Failure 173
1 Introduction 173
2 Fiber Bundle Model 174
3 Burst Statistics in the Fuse Model 179
4 Concluding Remarks 181
References 182
Scaling in Damage Accumulation 184
1 Accumulation of Radiation Defects and Thermofatigue Microcracks 185
2 Multiple Fracture Under Tension 187
3 Acoustic Properties of Low Carbon Steel Under Tension 190
4 Damage Evolution in the Earth Crust 191
References 193
Scaling of Effective Moduli of Generalised Continua 195
1 Introduction 195
2 Self-Similar and Fractal Approximations 197
3 Scaling of Effective Cosserat Moduli 200
4 Conclusions 202
References 203
An Influence of the Elastic Properties of Composite Components on the Mechanical Response of Polycrystalline Structures at Yield Level 205
1 Introduction 205
2 Formulation of the Problem 206
3 Numerical Examples 210
4 Conclusions 213
References 214
Statistical Length Scale in Weibull Strength Theory and Its Interaction with Other Scaling Lengths in Quasibrittle Failure 215
1 Introduction 215
2 ClassicalWeibull Strength Theory 216
3 Strength of Fiber Bundles 219
4 Strength of Chains of Fiber Bundles 220
5 Discussion and Relations to Strength of Quasibritlle Structures 225
References 226
Finite Fracture Mechanics for Fractal Cracks 228
1 Introduction 228
2 Finite Fracture Mechanics 228
3 Fractal Cracks with Finite Growth 230
4 Prediction of The Mirror-Mist-Hackle Phenomenon 233
5 Conclusions 235
References 235
Fractal Geometry and Mechanics of Randomly Folded Thin Sheets 237
1 Introduction and Background 237
2 Statistical Geometry of Folding 238
3 Mechanical Properties of Folded Sheets 243
References 245
Contact Mechanics at the Insect-Plant Interface: How Do Insects Stick and How Do Plants Prevent This? 246
1 Contact Problem 246
2 Hairy Attachment Devices 247
3 Anti-Adhesive Plant Surfaces 250
4 Conclusions 253
References 254
Morphological Evolution of Inhomogeneities Due to Diffusion and Epitaxy 256
1 Introduction 256
2 Formulation 257
3 Instabilities of Interface and Surface 259
4 Numerical Results 262
5 Conclusions 263
References 264
Some New Results on Fibre Models 265
1 Introduction 265
2 Shear Failure of Glued Interfaces 266
3 Bundle of Plastic Fibers 269
4 Fiber Bundle Model for Fatigue Failure 272
5 Concluding Remarks 273
References 274
Self-Similar Structural Systems with No-Unloading and Scale-Invariant Strength Distributions 275
1 Introduction 276
2 Multi-Element Systems with Random Element Strength 276
3 Hierarchical Bundle of Fibres and Multiscale Failure Modelling 282
4 Conclusion 288
References 288
Scaling and Hierarhical Structure of Cohesive Agglomerates of Nanoparticles 289
1 Introduction 289
2 Structure of Particle Agglomerates and Energy Dissipation 290
3 Scaling of Simple Agglomerates 294
4 Conclusion 298
References 298
Size-Dependent Bending of Thin Metallic Films 300
1 Introduction 300
2 Pure Bending of Macro-Plates 301
3 Pure Bending of Micro-Plates 304
4 Bending of Nano-Plates 306
5 Conclusions 309
References 309