Borodich IUTAM Symposium on Scaling in Solid Mechanics

Proceedings of the IUTAM Symposium held in Cardiff, UK, 25-29 June, 2007
1. Auflage 2008
ISBN: 978-1-4020-9033-2
Verlag: Springer Netherlands
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, Band 10, 310 Seiten

Reihe: IUTAM Bookseries

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 signicance. 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.

Autoren/Hrsg.

Borodich, F. M.

Inhaltsverzeichnis

1;Preface;5
2;Contents;7
3;Contributors;10
4;Universal Effective Toughness Distribution for Heterogeneous Brittle Materials;14
4.1;1 Introduction;14
4.2;2 Crack Depinning as a Critical Phenomenon;15
4.3;3 Analysis of Indentation Data;19
4.4;4 Conclusions;21
4.5;References;22
5;Scaling Transformations in Solid Mechanics;24
5.1;1 Introduction;24
5.2;2 Similarity, Dimensional Analysis and Homogeneity;26
5.3;3 Non-Classical Scalings;30
5.4;4 Conclusion;37
5.5;References;37
6;Mathematical Foundations of Non-Classical Extensions of Similarity Theory;40
6.1;1 Introduction;40
6.2;2 Non-Classical Extensions;42
6.3;3 Summary;46
6.4;4 Conclusion;47
6.5;References;47
7;Perturbing Paths of Slow Cracks in PMMA by Local Heating;49
7.1;1 Introduction;49
7.2;2 Experimental Procedures;50
7.3;3 Quasi-Static Cracks Under Tensile Loading;53
7.4;4 Redirection of Quasi-Static Cracks Using Secondary Loading;56
7.5;5 Discussion;58
7.6;References;59
8;Multiscale Hybrid Materials with Negative Poisson’s Ratio;60
8.1;1 Introduction;60
8.2;2 Negative Poisson’s Ratio in Granulate Materials;62
8.3;3 Negative Poisson’s Ratio of Material with Multiscale Distribution of Non-Sliding Cracks;64
8.4;4 Hybrid Material with Multiscale Distribution of Negative Poisson’s Ratio Inclusions;66
8.5;5 Conclusions;67
8.6;References;68
9;Modelling of Size Effects with Gradient-Enriched Continuum Theories;70
9.1;1 Introduction;70
9.2;2 Gradient Theories;71
9.3;3 Strain Concentrations in the Elastic Field;72
9.4;4 Peak Loads of Notched and Unnotched Beams;74
9.5;5 Energy Dissipation in Elementary Volumes;76
9.6;6 Conclusions;78
9.7;References;79
10;Internal Variables and Scale Separation in Dynamics of Microstructured Solids;80
10.1;1 Introduction;80
10.2;2 Local Balance Laws;81
10.3;3 Canonical Thermomechanics on the Material Manifold;82
10.4;4 Internal Variables;84
10.5;5 Scale Separation;86
10.6;6 Example: Microstructure in One-Dimension;87
10.7;7 Conclusions;90
10.8;References;90
11;On Rational Boundary Conditions for Higher-Order Long-Wave Models;92
11.1;1 Introduction;92
11.2;2 Governing Equations;93
11.3;3 Essential Boundary Conditions;96
11.4;4 Concluding Remarks;100
11.5;References;100
12;Scaling of Physical Processes in Fluid-Driven Fracture: Perspective from the Tip;102
12.1;1 Introduction;102
12.2;2 The Tip Boundary Layer Problem;103
12.3;3 Scaling of Non-Dominant Processes in the Global Fracture Solution;106
12.4;References;110
13;Space and Time Scaling Laws Induced by the Multiscale Fracturing of The Arctic Sea Ice Cover;112
13.1;1 Introduction;112
13.2;2 Scaling of Sea Ice Dispersion and Deformation;113
13.3;3 A Multiscale Statistical Model of Sea Ice Fracturing and Deformation;114
13.4;4 The Contribution of Small vs Large Events to Global Sea Ice Deformation;118
13.5;5 Conclusion;119
13.6;References;119
14;Similarity Approach to Hertz Type Contact Problems;121
14.1;1 Introduction;121
14.2;2 The Classic Elastic Contact Problems;122
14.3;3 Contact Problem Between a Punch and an Incompressible Isotropic Plastic (Nonlinearly Elastic) Half-Space;125
14.4;4 Contact Problems in the Case of Linear Creep of Materials;126
14.5;5 Generalizations of Similarity Methods in Hertz Type Contact;127
14.6;6 Self-Similar Problems of Elastic Contact for Non-Convex Punches;128
14.7;7 Some Engineering Applications;129
14.8;8 Conclusion;130
14.9;References;131
15;Multiscale Modelling in Contact Mechanics;133
15.1;1 Introduction;133
15.2;2 Two-Scales Analysis in Normal Contact of Elastic Bodies with Rough Surfaces;134
15.3;3 Multiscale Approach toWear Modeling;137
15.4;4 Conclusions;143
15.5;References;143
16;Recent Progress in Energetic Probablistic Scaling Laws for Quasi-Brittle Fracture;145
16.1;1 Introduction;145
16.2;2 Conspectus of Main Results;146
16.3;3 Review of Size Effect in Weakest Link Model and Its Asymptotics;149
16.4;4 Size Effect on Mean Strength via Asymptotic Matching;150
16.5;5 Grafted Weibull-Gaussian Strength Distribution for any Size;151
16.6;6 Size Effect on Structure Lifetime;152
16.7;7 Closing Comments;154
16.8;References;154
17;The Fractal-Statistical Nature of Size-Scale Effects on Material Strength and Toughness;155
17.1;1 Introduction;155
17.2;2 Size Scale-Effect on the Tensile Strength of Bodies Containing Many Imperfections;156
17.3;3 Size-Scale Effect on Fracture Energy of Grained Materials;158
17.4;4 The Case of Imperfect Similarity;160
17.5;5 On the Upper Cut-Off of the Maximum Defect (or Grain) Size;161
17.6;6 Monte Carlo Numerical Simulations;162
17.7;7 Conclusions;163
17.8;References;164
18;Scaling Laws for Properties of Materials with Imperfect Interfaces;166
18.1;1 Introduction;166
18.2;2 Scaling Laws for Elastic Properties;167
18.3;3 Scaling Laws for Conductivities;169
18.4;4 Conclusions;171
18.5;References;171
19;Burst Statistics as a Criterion for Imminent Failure;173
19.1;1 Introduction;173
19.2;2 Fiber Bundle Model;174
19.3;3 Burst Statistics in the Fuse Model;179
19.4;4 Concluding Remarks;181
19.5;References;182
20;Scaling in Damage Accumulation;184
20.1;1 Accumulation of Radiation Defects and Thermofatigue Microcracks;185
20.2;2 Multiple Fracture Under Tension;187
20.3;3 Acoustic Properties of Low Carbon Steel Under Tension;190
20.4;4 Damage Evolution in the Earth Crust;191
20.5;References;193
21;Scaling of Effective Moduli of Generalised Continua;195
21.1;1 Introduction;195
21.2;2 Self-Similar and Fractal Approximations;197
21.3;3 Scaling of Effective Cosserat Moduli;200
21.4;4 Conclusions;202
21.5;References;203
22;An Influence of the Elastic Properties of Composite Components on the Mechanical Response of Polycrystalline Structures at Yield Level;205
22.1;1 Introduction;205
22.2;2 Formulation of the Problem;206
22.3;3 Numerical Examples;210
22.4;4 Conclusions;213
22.5;References;214
23;Statistical Length Scale in Weibull Strength Theory and Its Interaction with Other Scaling Lengths in Quasibrittle Failure;215
23.1;1 Introduction;215
23.2;2 ClassicalWeibull Strength Theory;216
23.3;3 Strength of Fiber Bundles;219
23.4;4 Strength of Chains of Fiber Bundles;220
23.5;5 Discussion and Relations to Strength of Quasibritlle Structures;225
23.6;References;226
24;Finite Fracture Mechanics for Fractal Cracks;228
24.1;1 Introduction;228
24.2;2 Finite Fracture Mechanics;228
24.3;3 Fractal Cracks with Finite Growth;230
24.4;4 Prediction of The Mirror-Mist-Hackle Phenomenon;233
24.5;5 Conclusions;235
24.6;References;235
25;Fractal Geometry and Mechanics of Randomly Folded Thin Sheets;237
25.1;1 Introduction and Background;237
25.2;2 Statistical Geometry of Folding;238
25.3;3 Mechanical Properties of Folded Sheets;243
25.4;References;245
26;Contact Mechanics at the Insect-Plant Interface: How Do Insects Stick and How Do Plants Prevent This?;246
26.1;1 Contact Problem;246
26.2;2 Hairy Attachment Devices;247
26.3;3 Anti-Adhesive Plant Surfaces;250
26.4;4 Conclusions;253
26.5;References;254
27;Morphological Evolution of Inhomogeneities Due to Diffusion and Epitaxy;256
27.1;1 Introduction;256
27.2;2 Formulation;257
27.3;3 Instabilities of Interface and Surface;259
27.4;4 Numerical Results;262
27.5;5 Conclusions;263
27.6;References;264
28;Some New Results on Fibre Models;265
28.1;1 Introduction;265
28.2;2 Shear Failure of Glued Interfaces;266
28.3;3 Bundle of Plastic Fibers;269
28.4;4 Fiber Bundle Model for Fatigue Failure;272
28.5;5 Concluding Remarks;273
28.6;References;274
29;Self-Similar Structural Systems with No-Unloading and Scale-Invariant Strength Distributions;275
29.1;1 Introduction;276
29.2;2 Multi-Element Systems with Random Element Strength;276
29.3;3 Hierarchical Bundle of Fibres and Multiscale Failure Modelling;282
29.4;4 Conclusion;288
29.5;References;288
30;Scaling and Hierarhical Structure of Cohesive Agglomerates of Nanoparticles;289
30.1;1 Introduction;289
30.2;2 Structure of Particle Agglomerates and Energy Dissipation;290
30.3;3 Scaling of Simple Agglomerates;294
30.4;4 Conclusion;298
30.5;References;298
31;Size-Dependent Bending of Thin Metallic Films;300
31.1;1 Introduction;300
31.2;2 Pure Bending of Macro-Plates;301
31.3;3 Pure Bending of Micro-Plates;304
31.4;4 Bending of Nano-Plates;306
31.5;5 Conclusions;309
31.6;References;309