University of Minnesota
Aerospace Engineering and Mechanics
Spring 1999 Seminar Series

Fractals and fractal scaling in fracture mechanics

Professor Feodor Borodich

Department of Mathematics, Glasgow Caledonian University

Fractals are a very popular concept in modern physics. Almost everyone has heard about fractals. However, what really works in fractal theory and what is simply wishful thinking and beautiful frills? An attempt to answer the question is given in the talk. Some definitions and methods attributed to fractal geometry are reviewed and the difference between mathematical and physical fractals is emphasized. A review of modern fractal models of fracture in brittle and quasibrittle materials is given. The scaling for both a fractal solitary crack and a fractal pattern of microcracks surrounding the main fracture is considered. Some author's concepts appropriate for fractal description of fracture are discussed. It is shown that if the layer of inelastic deformations in quasibrittle materials has the same order of magnitude as the upper cutoff of the fractal scaling then fractal properties of the main crack surface do not correlate with fracture energy. This observation selects the cases when the concept of the universal roughness exponent may be valid. It is shown that the correlation between fractal properties of a pattern of microcracks and the fracture energy of polyphase materials is usually possible.

Friday, June 4, 1999
209 Akerman Hall
2:30-3:30 p.m.

Refreshments served after the seminar in 227 Akerman Hall.
Disability accomodations provided upon request.
Contact Kristal Belisle, Senior Secretary, 625-8000.