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

Table of Contents:
Universal Effective Toughness Distribution for Heterogeneous Brittle Materials.- Scaling Transformations in Solid Mechanics.- Mathematical Foundations of Non-Classical Extensions of Similarity Theory.- Perturbing Paths of Slow Cracks in PMMA by Local Heating.- Multiscale Hybrid Materials with Negative Poisson’s Ratio.- Modelling of Size Effects with Gradient-Enriched Continuum Theories.- Internal Variables and Scale Separation in Dynamics of Microstructured Solids.- On Rational Boundary Conditions for Higher-Order Long-Wave Models.- Scaling of Physical Processes in Fluid-Driven Fracture: Perspective from the Tip.- Space and Time Scaling Laws Induced by the Multiscale Fracturing of The Arctic Sea Ice Cover.- Similarity Approach to Hertz Type Contact Problems.- Multiscale Modelling in Contact Mechanics.- Recent Progress in Energetic Probablistic Scaling Laws for Quasi-Brittle Fracture.- The Fractal-Statistical Nature of Size-Scale Effects on Material Strength and Toughness.- Scaling Lawsfor Properties of Materials with Imperfect Interfaces.- Burst Statistics as a Criterion for Imminent Failure.- Scaling in Damage Accumulation.- Scaling of Effective Moduli of Generalised Continua.- An Influence of the Elastic Properties of Composite Components on the Mechanical Response of Polycrystalline Structures at Yield Level.- Statistical Length Scale in Weibull Strength Theory and Its Interaction with Other Scaling Lengths in Quasibrittle Failure.- Finite Fracture Mechanics for Fractal Cracks.- Fractal Geometry and Mechanics of Randomly Folded Thin Sheets.- Contact Mechanics at the Insect-Plant Interface: How Do Insects Stick and How Do Plants Prevent This?.- Morphological Evolution of Inhomogeneities Due to Diffusion and Epitaxy.- Some New Results on Fibre Models.- Self-Similar Structural Systems with No-Unloading and Scale-Invariant Strength Distributions.- Scaling and Hierarhical Structure of Cohesive Agglomerates of Nanoparticles.- Size-Dependent Bending of Thin Metallic Films.