Abstract
In a number of occasions, one is interested in characterizing and understanding the behavior of heterogeneous materials on a scale much larger than that of the elementary constituents. When the local behavior is linear (elasticity, conductivity, permeability, …) the macroscopic behavior will also be linear, and with very few restrictions, the macroscopic properties will converge under coarse graining toward a well defined limit, justifying the powerful concept of equivalent homogeneous medium. However, when the local properties are non-linear, it may happen that the macroscopic behavior will be controlled by the heterogeneities of the medium at all scales. This turns out to be the case for instance in brittle fracture. Other examples may also be found in various frameworks: critical currents in disordered superconductors, clogging of porous filters by deposition of particles in pores, flow of threshold fluids in a porous medium, plastic behavior of heterogeneous solids, etc … In many a case, it is possible to distinguish different regimes for the local behavior, and thus different “phases”, and the geometrical arrangement of these phases produces naturally patterns which reveal some information about the development of the structure, and thus the complex interactions at play at the local scale.
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, North-Holland, (Amsterdam, 1990)
J. C. Charmet, S. Roux and E. Guyon eds., Disorder and Fracture, Plenum, (New York, 1990)
P. M. Duxbury, P. D. Beale and P. L. Leath, Phys. Rev. Lett. 57, 1052,(1986); P. M. Duxbury, P. L. Leath and P. D. Beale, Phys. Rev. B 36, 367, (1987).
L. Niemeyer, L. Pietronero, H. J. Weissman, Phys. Rev. Lett. 52, 1033, (1984).
M. Sahimi and J. D. Goddard, Phys. Rev. B 33, 7848, (1986).
E. Louis and F. Guinea, Europhys. Lett. 3, 871, (1987).
L. de Arcangelis, A. Hansen, H. J. Herrmann and S. Roux, Phys. Rev. B 40, 877,(1989).
R. L. Smith and S. L. Phoenix, J. App. Mech. 48, 75, (1981).
W. A. Curtin and H. Scher, J. Mater. Res. 5, 535, (1990).
P. Rossi and S. Richer, Mat. and Struct. 20, 334, (1987).
P. Meakin, Cryst. Prop. and Prep. 17, 1, (1988).
P. D. Beale and D. J. Srolovitz, Phys. Rev. B 37, 5500, (1988).
L. de Arcangelis and H. J. Herrmann, Phys. Rev. B 39, 2678, (1989).
H. J. Herrmann, A. Hansen and S. Roux, Phys. Rev. B 39, 637, (1989).
A. Hansen, S. Roux and H. J. Herrmann, J. Physique (Paris) 50, 733, (1989).
T. C. Halsey, M. H. Jenssen, L. P. Kadanoff, I. Procaccia and B. I. Shraiman, Phys. Rev. A 33, 1141, (1986).
S. Roux, A. Hansen, H. J. Herrmann and E. Guyon, J. Stat. Phys. 52, 237, (1988).
L. de Arcangelis, S. Redner and A. Coniglio, Phys. Rev. B 31, 4725, (1985).
A. Hansen, E. L. Hinrichsen and S. Roux, Europhys. Lett. 13, 517, (1990).
Y. Berthaud, E. Ringot and D. Fokwa, Cement and Concrete Research, 21, 928, (1991).
S. Roux and A. Hansen, Europhys. Lett. 8, 729, (1989).
S. Roux and A. Hansen, in Ref.[2] p.17; S. Roux, A. Hansen and E. L. Hinrichsen, preprint.
A. Hansen, E. L. Hinrichsen and S. Roux, Phys. Rev. B 43, 665, (1991).
S. Roux and A. Hansen, Europhys. Lett. 11, 37, (1990).
A. Hansen, E. L. Hinrichsen and S. Roux, Phys. Rev. Lett. 66, 2476, (1991).
B. B. Mandelbrot, D. E. Passoja and A. J. Paullay Nature 308, 721, (1984).
E. Bouchaud, G. Lapasset and J. Planés, Europhys. Lett. 13, 73, (1990).
K. J. Måløy, A. Hansen, E.L. Hinrichsen and S. Roux, preprint.
S. Gentier, Private communication.
J. Schmittbuhl, Y. Berthaud and S. Roux, Compte-Rendu du GRECO Géomatériaux, (1991).
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1993 Springer Science+Business Media New York
About this chapter
Cite this chapter
Roux, S. (1993). Growth Patterns in Fracture. In: Garcia-Ruiz, J.M., Louis, E., Meakin, P., Sander, L.M. (eds) Growth Patterns in Physical Sciences and Biology. NATO ASI Series, vol 304. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-2852-4_31
Download citation
DOI: https://doi.org/10.1007/978-1-4615-2852-4_31
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4613-6235-7
Online ISBN: 978-1-4615-2852-4
eBook Packages: Springer Book Archive