Symposium on Scaling in Solid Mechanics
25 June 2007
Ends: 29 June 2007
The symposium will address theoretical, experimental and computational issues in scaling. Scaling methods apply wherever there is similarity across many scales. The similarity may be found in geometry or in the evolution of a process. In contrast to fluid mechanics, scaling in solid mechanics has been restricted for a long time to just the equivalence of nondimensional parameters characterising the problem, while other scaling techniques were neglected. However, a wealth of empirical rules usually expressed as power laws, have been established indicating that various processes of solid mechanics are self-similar. This supports the idea that natural processes in a surprisingly large number of cases are, broadly speaking, self-similar in their intermediate stages when the behaviour of the processes has ceased to depend on the details of the boundary or initial conditions. These processes include damage accumulation, growth of fatigue cracks, development of patterns of flaws in the earth’s core or in ice, abrasiveness of rough surfaces, and so on. Some of the power laws may also be related to fractal features of the process.
Several modern theories of solids that involve an internal characteristic length are another area of application of scaling. In these theories, scaling laws allow bridging of the scales. Extensive studies over the last twenty years or so have shown that scaling is a powerful tool for solving various problems of solid mechanics and related areas. Scaling is a rapidly expanding area of research having multidisciplinary applications, e.g. various new techniques bridging the nanoscale and macroscale have been recently introduced in materials science and fracture mechanics. Papers are encouraged, but not restricted to, the following themes: incomplete self-similarity, parametric-homogeneity, multiscale analysis, similarity transformations, renormalization techniques, and fractals in application to fracture mechanics, contact problems, geophysics and other areas of solid mechanics.
Open To: Staff and Students