# University of Minnesota

Aerospace Engineering and Mechanics

**Spring 1999 Seminar Series**

*Fractals and fractal scaling in fracture mechanics*

*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.