Abstract
The propagation of a crack in an isotropic elastic medium is treated as a moving boundary problem. Linear stability analysis shows that for the stretched membrane with a central, initially circular hole all modes are stable. On the other hand all modes are unstable for a two-dimensional arrangement where the crack is induced by pressure in a central hole. Numerical simulations of beam lattices yield fractal crack patterns since the instabilities are enhanced by the heterogeneities of the material. Particularly successful for the numerical implementation is the use of vectorized random lattices. The ensemble of cracks generated under increasing load is shown to follow scaling laws in the size of the sample.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
H.J. Herrmann and S. Roux (eds.), Statistical Models for the Fracture of Disordered Media ( Elsevier, Amsterdam, 1990 )
T. Vicsek, Fractal Growth, Phenomena ( World Scientific, Singapore, 1988 )
J. Kertész in Ref. 1, p.261
H.J. Herrmann, J. Kertész arid L. de Arcangelis, Europhys. Lett. 10, 117 (1989)
W.W. Mullins and R.F. Sekerka, J. Appt Phys. 34, 323 (1963)
P.G. Saifmann and G.I. Taylor, Proc. R. Soc. London A. 255, 312 (1957)
H.J. Herrmann in Random Fluctuations in Pattern Growth, eds. H.E. Stanley and N. Ostrowski, (NATO AST Series Vol.157, Kluwer, Dordrecht, 1988 ), p. 149
R. Van Damme, E. Alsa.c and C. Laroe, Comptes Rendus Acad. Sci., Série II 309, 11 (1988)
H. Van Darnme, in The Fractal Approach to Heterogeneous Chemistry, D. Avnir (ed.), p. 199, ( Wiley, 1989 )
L.D. Landau and E.M. Lifschitz, Elasticity (Pergamon, 1960 ), p. 130
M. Barber, J. Donley and J.S. Langer, Phys. Rev. A40, 366 (1989)
H. R. Ball and R. Blumenfeld, Phys. Rev. Lett. 65, 1764 (1990)
H.J. Herrmann and J. Kertész, Physica, A 178, 227 (1992)
D.A. Kessler, J. Koplik and H. Levine, Adv. Phys. 37, 255 (1988)
S. Roux and E. Guyon, J. Physique Lett. 46, L999 (1985)
R.J. Roark and W.C. Young, Formulas for Stress and Strain, ( Mc Craw Hill, Tokyo, 1975 ), p. 89
Numerical Recipes, The Art of Scientific Computing, W.H. Press, B.P. Flannery, S.A. Teukolsky and W.T. Vetterling (Cambridge Univ. Press, 1986 )
E. Louis, F. Guinea and F. Flores, in Fractals in Physics, L. Pietronero and E. Tossatti (eds.) ( Elsevier, Amsterdam, 1986 )
E. Louis and F. Guinea, Europhys. Lett. 3, 871 (1987);
P. Meakin, G. Li, L.M. Sander, E. Louis and F. Guinea, J. Phys. A 22, 1393 (1989);
E.L. Hinrichsen, A. Hansen and S. Roux, Europhys. Lett. 8, 1 (1989)
S. Roux, J. Stat. Phys. 48, 201 (1987)
P. Ossa.dnik, preprint
M.J. Blackburn, W.H. Srnyrl 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
C. Moukarzel and H.J. Herrmann, J. Stat. Phys.
E. Schlangen and J.G.M. van Mier, preprint
H.J. Herrmann, A. Hansen and S. Roux, Phys. Rev. B 39, 637 (1989)
H J. Herrmann, in NATO workshop “Growth Patterns in Physical Sciences and Biology” (Granada, 1991)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1993 Springer Science+Business Media Dordrecht
About this chapter
Cite this chapter
Herrmann, H.J. (1993). Crack Patterns: Generalized Laplacian Structures. In: Schneider, G.A., Petzow, G. (eds) Thermal Shock and Thermal Fatigue Behavior of Advanced Ceramics. NATO ASI Series, vol 241. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-8200-1_12
Download citation
DOI: https://doi.org/10.1007/978-94-015-8200-1_12
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-481-4291-0
Online ISBN: 978-94-015-8200-1
eBook Packages: Springer Book Archive