Title: Similarity and Fractals in Contact and Nano Mechanics
Speaker: Feodor Borodich
Speaker Info: Northwestern University
Brief Description:
Special Note: More current information may be available at Plan-it Purple
Abstract:
It is known that natural processes in a surprisingly large number of cases are, broadly speaking, self-similar on their intermediate stage of development. Two objects are similar if one can be obtained from another by some transformation. Usually, the transformation is the coordinate dilations. For example, two triangles are similar if one can be transformed into another one by magnification (dilation), rotation, and translation. The idea of similarity is undergoing the upsurge of interest due to the introducing the concept of fractals. However, similarity is not just fractals. Fractal concepts, parametric homogeneity and other non-traditional similarity ideas are discussed in detail. Various applications of similarity methods to problems of contact and nano mechanics are considered. These applications include the Hertz type contact problems and nano-indentation tests, models of contact for fractal punches, and recent results concerning abrasion wear of a steel ball by nano-sharp asperities of hard carbon containing coatings. The talk is targeted to non-specialists. All used concepts will be explained.Date: Friday, January 17, 2003