Abstract
Cracks are grown in a system submitted to external shear by solving the full Lamé equation on a two-dimensional lattice. One finds that deterministic fracture patterns are in general branched and can be fractal. This effect is due to the competition between the direction of global stress and the local growth direction imposed by the lattice anisotropy.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
See e.g. H. Liebowitz (ed.), Fracture, Vols. I–VII, (Academic Press, New York, 1984)
H.J. Herrmann in Random Fluctuations and Pattern Growth, eds. H.E. Stanley and N. Ostrowsky (Kluwer, Dordrecht, 1988), p.149
L. de Arcangelis, S. Redner and H.J. Herrmann, J. Physique Lett. 46, L585 (1985)
P.M. Duxbury, P.D. Beale and P.L. Leath, Phys. Rev. Lett. 57, 1052 (1986)
P.M. Duxbury and P.L. Leath, J. Phys. A 20, L411 (1987)
P.D. Beale and D.J. Srolovitz, Phys. Rev. B 37, 5500 (1988) and references therein
B. Kahng, G.G. Batrouni, S. Redner, L. de Arcangelis and H.J. Herrmann, Phys. Rev. B 37, 7625 (1988)
H.J. Herrmann, A. Hansen and S. Roux, Phys. Rev. B 39, 637 (1989) and references therein
T.A. Witten and L.M. Sander, Phys. Rev. Lett. 47, 1400 (1981)
L. Niemeyer, L. Pietronero and H.J. Wiesmann, Phys. Rev. Lett. 52, 1033 (1984)
E. Louis, F. Guinea and F. Flores in Fractals in Physics eds. L. Pietronero and E. Tossatti (Elsevier, Amsterdam, 1986), p.117
E. Louis and F. Guinea, Europhys. Lett. 3, 871 (1987)
E.L. Hinrichsen, A. Hansen and S. Roux, Europhys. Lett. 8, 1 (1989); P. Meakin, G. Li, L.M. Sander, E. Louis and F. Guinea, J.Phys. A to be published
L.D. Landau and E.M. Lifshitz, Theory of Elasticity (Pergamon, Oxford, 1986)
S. Roux and E. Guyon, J. Physique Lett. 46, L999 (1985)
G.G. Batrouni and A. Hansen, J. Stat. Phys. 52, 747 (1988)
C. Tang, Phys. Rev. A, 31, 1977 (1985)
J. Szép, J. Cserti and J. Kertész, J. Phys. A 18, L413 (1985)
J. Nittmann and H.E. Stanley, Nature 321, 661 (1986)
J. Kertész and T. Vicsek, J. Phys. A 19, L257 (1986)
J. Fernandez, F. Guinea and E. Louis, J. Phys. A 21, L301 (1988)
B.B. Mandelbrot and T. Vicsek, J. Phys. A to be published
H.J. Herrmann, J. Kertész and L. de Arcangelis, in preparation
F. Family, D.E. Platt and T. Vicsek, J. Phys. A 20, L1177 (1987)
J.P. Eckmann, P. Meakin, I. Procaccia and R. Zeitak, Phys. Rev. A preprint
M.J. Blackburn, W.H. Smyrl and J.A. Feeney, in Stress Corrosion in High Strength Steels and in Titanium and Aluminium Alloys, ed. B.F. Brown (Naval Res. Lab., Washington, 1972), p.344
H. Takayasu in Fractals in Physics, eds. L. Pietronero and E. Tossatti (Elsevier, Amsterdam, 1986), p. 181
H. Takayasu, Phys. Rev. Lett. 54, 1099 (1985)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1989 Springer Science+Business Media New York
About this chapter
Cite this chapter
Herrmann, H.J. (1989). Shapes of Deterministic Cracks Obtained under Shear. In: Pietronero, L. (eds) Fractals’ Physical Origin and Properties. Ettore Majorana International Science Series. Springer, Boston, MA. https://doi.org/10.1007/978-1-4899-3499-4_15
Download citation
DOI: https://doi.org/10.1007/978-1-4899-3499-4_15
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4899-3501-4
Online ISBN: 978-1-4899-3499-4
eBook Packages: Springer Book Archive