The fracturing of brittle solids using lattice models
yields complex crack shapes due to the disorder in the material.
The figure shows a
hydraulic crack produced with Frank Tzschichholz.
The stress distribution is visualized by birefingence patterns
numerically obtained from the eigenvalues of the tensor.
For more detail see our
paper in Phys. Rev. B, Vol.49, p.7056-7059 (1994).
In a further
work published in Physica Review E, Vol.51, p. 1961-1970
(1995) we obtained the pressure fluctuations and
acoustic emission signals in a two-dimensional hydraulic crack.
With Stephane Roux we edited in 1990 a book about fracture of heterogenoeus
materials entitled: "Statistical Models for the Fracture of Disordered Media"
which appeared in North Holland. In this book you find the following
article which reviews the scaling laws we discovered for
the brittle failure of heterogeneous solids. The original
article on the scaling of beam networks (with
published in Phys. Rev. B, Vol.39, p.637-648 (1989)
and on scalar networks including
Lucilla de Arcangelis was
in Phys. Rev. B, Vol.40, p.877-880 (1989).
Janos Kertesz and Lucilla de Arcangelis I was able to
find fractal cracks obtained under shear even without
in Europhys. Lett., Vol.10, p.147-152 (1989) by considering
at the crack surface the accumulation of damage. More details
about this are given in a
proceedings of a meeting in Erice 1988 published by Plenum Press
were in particular the application to corrosion stress cracking.
In fact with Victor Horwath we did measure the fractal dimension
of experimental corrosion cracks as
published in Chaos, Solitons and Fractals, Vol.1, p.395-400 (1992).
With Janos Kertesz I also studied the stability of a circular
hole in a stretched membrane using linear stability analysis as
published in Physica A, Vol.178, p.409-412 (1991).
In various occasions I reviewed the above works on fractures
example in the colourful book on Fractals edited by
Armin Bunde and Shlomo Havlin (Springer, 1991) or in an
article published in Physica A, Vol.221, p.125-133 (1995).