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.

This Volume constitutes the Proceedings of the IUTAM Symposium on 'Scaling Laws in Ice Mechanics and Ice Dynamics', held in Fairbanks, Alaska from 13th to 16th of June 2000. Ice mechanics deals with essentially intact ice: in this discipline, descriptions of the motion and deformation of Arctic/ Antarctic and river/lake ice call for the development of physically based constitutive and fracture models over an enormous range in scale: 0.01 m - 10 km. Ice dynamics, on the other hand, deals with the movement of broken ice: descriptions of an aggregate of ice floes call for accurate modeling of momentum transfer through the sea/ice system, again over an enormous range in scale: 1 km (floe scale) - 500 km (basin scale). For ice mechanics, the emphasis on lab-scale (0.01 - 0.5 m) research con trasts with applications at the scale of order 1 km (ice-structure interaction, icebreaking); many important upscaling questions remain to be explored.

This volume constitutes the Proceedings of the IUTAM Symposium on "Analytical and Computational Fracture Mechanics of Non-homogeneous Materials", held in Cardiff from 18th to 22nd June 2001. The Symposium was convened to address and place on record topical issues in analytical and computational aspects of the fracture of non-homogeneous materials as they are approached by specialists in mechanics, materials science and related fields. The expertise represented in the Symposium was accordingly very wide, and many of the world's greatest authorities in their respective fields participated. Given the extensive range and scale of non-homogeneous materials, it had to be focussed to enhance the quality and impact of the Symposium. The range of non-homogeneous materials was limited to those that are inhomogeneous at the macroscopic level and/or exhibit strain softening. The issues of micro to macro scaling were not excluded even within this restricted range which covered materials such as rock, concrete, ceramics and composites on the one hand, and, on the other, those metallic materials whose ductile fracture is strongly influenced by the presence of inhomogeneities. The Symposium remained focussed on fundamental research issues of practical significance. These issues have many common features among seemingly disparate non-homogeneous materials.

This volume is a collection of twenty five written contributions by distinguished invited speakers from seven countries to the IUTAM Symposium on Size Effects on Material and Structural Behavior at Micron- and Nano-scales. Size effects on material and structural behaviors are of great interest to physicists, material scientists, and engineers who need to understand and model the mechanical behavior of solids especially at micron- and nano-scales.

This volume contains the proceedings of the IUTAM Symposium on Mechanical Behavior and Micro-mechanics of Nanostructured Materials, held in Beijing on June 27-30, 2005. The proceedings consist of approximately 30 presentations. Nano-scale, micro-scale, theoretical, experimental and numerical aspects of the subjects are covered. A wide scope of research and progress are displayed. This is the first work in print on this particular subject.

This volume constitutes the proceedings of the IUTAM Symposium on Surface Effects in the Mechanics of Nanomaterials and Heterostructures, held in Beijing, 8-12 August, 2010. The symposium brought together the most active scientists working in this area from the fields of solid mechanics, composites, physics, and materials science and summarized the state-of-the-art research results with a view to advancing the frontiers of mechanics and materials physics. Nanomaterials and heterostructures have a large fraction of their atoms at surfaces and interfaces. These atoms see a different environment to those in the interior and can have a substantial effect on the overall mechanical and physical behaviour of a material. The last decade has witnessed a growing interest in the study of surfaces and how the surface behaviour couples with that of the bulk to determine the overall system response. The papers in this proceedings cover: extension of continuum mechanics and thermodynamics to the nano-scale; multiscale simulations; surface effects in monolithic nano-scale elements and nanostructures; mechanical and physical properties of nanomaterials and heterostructures; self-assembly, etc. The surface stress effect is inherently a multidisciplinary and fertile field; the Symposium truly reflects these features. This IUTAM Symposium was also dedicated to Professor Bhushan L Karihaloo of Cardiff University on his impending retirement, in recognition of his contributions to the fields of solid mechanics and nanomechanics, and to IUTAM activities in general.

This volume presents selected papers from the IUTAM Symposium on Reynolds Number Scaling in Turbulent Flow, convened in Princeton, NJ, USA, September I1-13, 2002. The behavior ofturbulence at high Reynolds number is interesting from a fundamental point of view, in that most theories of turbulence make very specific predictions in the limit of infinite Reynolds number. From a more practical point of view, there exist many applications that involve turbulent flow where the Reynolds numbers are extremely large. For example, large vehicles such as submarines and commercial transports operate at Reynolds 9 numbers based on length ofthe order oft0 , and industrial pipe flows cover a 7 very wide range of Reynolds numbers up to 10 • Many very important applications of high Reynolds number flow pertain to atmospheric and other geophysical flows where extremely high Reynolds numbers are the rule rather than the exception, and the understanding of climate changes and the prediction of destructive weather effects hinges to some extent on our appreciation ofhigh-Reynolds number turbulence behavior. The important effects of Reynolds number on turbulence has received a great deal of recent attention. The objective of the Symposium was to bring together many of the world's experts in this area to appraise the new experimental results, discuss new scaling laws and turbulence models, and to enhance our mutual understanding of turbulence.