IUTAM Symposium on Scaling in Solid Mechanics (eBook)

Proceedings of the IUTAM Symposium held in Cardiff, UK, 25-29 June, 2007

F. M. Borodich (Herausgeber)

eBook Download: PDF

2008 | 2009
XIV, 310 Seiten
Springer Netherland (Verlag)
978-1-4020-9033-2 (ISBN)

Infos

This volume constitutes the Proceedings of the IUTAM Symposium on 'Scaling in Solid Mechanics', held in Cardiff from 25th to 29th June 2007. The Symposium was convened to address and place on record topical issues in theoretical, experimental and computational aspects of scaling approaches to solid mechanics and related elds. Scaling is a rapidly expanding area of research having multidisciplinary - plications. The expertise represented in the Symposium was accordingly very wide, and many of the world's greatest authorities in their respective elds participated. Scaling methods apply wherever there is similarity across many scales or one need to bridge different scales, e. g. the nanoscale and macroscale. The emphasis in the Symposium was upon fundamental issues such as: mathematical foundations of scaling methods based on transformations and connections between multi-scale approaches and transformations. The Symposium remained focussed on fundam- tal research issues of practical signi cance. The considered topics included damage accumulation, growth of fatigue cracks, development of patterns of aws in earth's core and inice, abrasiveness of rough surfaces, and soon. The Symposium consisted of forty-two oral presentations. All of the lectures were invited. Full record of the programme appears as an Appendix. Several of the lectures are not represented, mainly because of prior commitments to publish elsewhere. The proceedings p- vide a reasonable picture of understanding as it exists at present. The Symposium showed that scaling methods cannot be reduced solely to dimensional analysis and fractal approaches.

Inhalt

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

Produkt-Details

• Erscheint lt. Verlag: 14.11.2008
• Reihe/Serie: IUTAM Bookseries
• Reihe/Serie: IUTAM Bookseries
• Zusatzinfo: XIV, 310 p.
• Verlagsort: Dordrecht
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Mathematik ► Angewandte Mathematik
• Themenwelt: Mathematik / Informatik ► Mathematik ► Statistik
• Themenwelt: Mathematik / Informatik ► Mathematik ► Wahrscheinlichkeit / Kombinatorik
• Themenwelt: Naturwissenschaften ► Physik / Astronomie ► Mechanik
• Themenwelt: Technik ► Bauwesen
• Themenwelt: Technik ► Maschinenbau
• Schlagworte: Development • Geometry • IUTAM • linear optimization • Mechanics • Metall • microstructure • Modeling • scaling • solid mechanics • Statistics • Transformation
• ISBN-10: 1-4020-9033-1 / 1402090331
• ISBN-13: 978-1-4020-9033-2 / 9781402090332