IUTAM Symposium on Scaling in Solid Mechanics: Proceedings of the IUTAM Symposium held in Cardiff, UK, 25-29 June, 2007 (IUTAM Bookseries (10))

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 fields. Scaling is a rapidly expanding area of research having multidisciplinaryapplications. The expertise represented in the Symposium was accordingly very wide, and many of the world's greatest authorities in their respective fields participated. Scaling methods apply wherever there is similarity across many scales or a 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 fundamental research issues of practical significance. The topics considered included damage accumulation, growth of fatigue cracks, development of patterns of flaws in the earth's core and in ice, abrasiveness of rough surfaces, and so on. The Symposium showed that scaling methods cannot be reduced solely to dimensional analysis and fractal approaches. Modern scaling approaches consist of a great diversity of techniques. These proceedings contain lectures on state-of-the-art developments in self-similar solutions, fractal models, models involving interplay between different scales, size effects in fracture of solids and bundles of fibres, scaling in problems of fracture mechanics, nanomechanics, contact mechanics and testing of materials by indentation, scaling issues in mechanics of agglomeration of adhesive particles, and in biomimetic of adhesive contact. Contents......Page 8 Universal Effective Toughness Distribution for Heterogeneous Brittle Materials......Page 15 Scaling Transformations in Solid Mechanics......Page 25 Mathematical Foundations of Non-Classical Extensions of Similarity Theory......Page 41 Perturbing Paths of Slow Cracks in PMMA by Local Heating......Page 50 Multiscale Hybrid Materials with Negative Poisson's Ratio......Page 61 Modelling of Size Effects with Gradient-Enriched Continuum Theories......Page 71 Internal Variables and Scale Separation in Dynamics of Microstructured Solids......Page 81 On Rational Boundary Conditions for Higher-Order Long-Wave Models......Page 93 Scaling of Physical Processes in Fluid-Driven Fracture: Perspective from the Tip......Page 103 Space and Time Scaling Laws Induced by the Multiscale Fracturing of The Arctic Sea Ice Cover......Page 113 Similarity Approach to Hertz Type Contact Problems......Page 122 Multiscale Modelling in Contact Mechanics......Page 134 Recent Progress in Energetic Probablistic Scaling Laws for Quasi-Brittle Fracture......Page 146 The Fractal-Statistical Nature of Size-Scale Effects on Material Strength and Toughness......Page 156 Scaling Laws for Properties of Materials with Imperfect Interfaces......Page 167 Burst Statistics as a Criterion for Imminent Failure......Page 174 Scaling in Damage Accumulation......Page 185 Scaling of Effective Moduli of Generalised Continua......Page 196 An Influence of the Elastic Properties of Composite Components on the Mechanical Response of Polycrystalline Structures at Yield Level......Page 206 Statistical Length Scale in Weibull Strength Theory and Its Interaction with Other Scaling Lengths in Quasibrittle Failure......Page 216 Finite Fracture Mechanics for Fractal Cracks......Page 229 Fractal Geometry and Mechanics of Randomly Folded Thin Sheets......Page 238 Contact Mechanics at the Insect-Plant Interface: How Do Insects Stick and How Do Plants Prevent This?......Page 247 Morphological Evolution of Inhomogeneities Due to Diffusion and Epitaxy......Page 257 Some New Results on Fibre Models......Page 266 Self-Similar Structural Systems with No-Unloading and Scale-Invariant Strength Distributions......Page 276 Scaling and Hierarhical Structure of Cohesive Agglomerates of Nanoparticles......Page 290 Size-Dependent Bending of Thin Metallic Films......Page 301 This volume constitutes the Proceedings of the IUTAM Symposium on 'Scaling in Solid Mechanics', held in Cardiff from 25th to 29th June 2007, to address topical issues in theoretical, experimental and computational aspects of scaling approaches to solid mechanics and related fields. Scaling is a rapidly expanding area of research which has multidisciplinary applications. The expertise represented at the Symposium was accordingly very wide, and many of the world's greatest authorities in their respective fields participated. Scaling methods apply wherever there is similarity across many scales or a need to bridge different scales, e.g. the nanoscale and macroscale. The emphasis at the Symposium was on 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 fundamental research issues of practical significance. The topics considered included damage accumulation, growth of fatigue cracks, development of patterns of flaws in the earth's core and in ice, abrasiveness of rough surfaces, and so on. The Symposium showed that scaling methods cannot be reduced solely to dimensional analysis and fractal approaches. Modern scaling approaches consist of a great diversity of techniques. These proceedings contain lectures on state-of-the-art developments in self-similar solutions, fractal models, models involving interplay between different scales, size effects in fracture of solids and bundles of fibres, scaling in problems of fracture mechanics, nanomechanics, contact mechanics and testing of materials by indentation, scaling issues in mechanics of agglomeration of adhesive particles, and in biomimetic of adhesive contact