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Hierarchical crack pattern as formed by successive domain divisions. II. From disordered to deterministic behavior
 

Summary: Hierarchical crack pattern as formed by successive domain divisions. II. From disordered
to deterministic behavior
S. Bohn*
Laboratoire de Physique Statistique, École Normale Supérieure, 24 Rue Lhomond, 75231 Paris Cedex 05, France
and Magnasco Lab, The Rockefeller University, Box 212, 1230 York Avenue, New York, New York 10021, USA
J. Platkiewicz, B. Andreotti, M. Adda-Bedia, and Y. Couder
Laboratoire de Physique Statistique, École Normale Supérieure, 24 Rue Lhomond, 75231 Paris Cedex 05, France
Received 8 December 2004; published 28 April 2005
Hierarchical crack patterns, such as those formed in the glaze of ceramics or in desiccated layers of mud or
gel, can be understood as a successive division of two-dimensional domains. We present an experimental study
of the division of a single rectangular domain in drying starch and show that the dividing fracture essentially
depends on the domain size, rescaled by the thickness of the cracking layer e. Utilizing basic assumptions
regarding the conditions of crack nucleation, we show that the experimental results can be directly inferred
from the equations of linear elasticity. Finally, we discuss the impact of these results on hierarchical crack
patterns, and in particular the existence of a transition from disordered cracks at large scales--the first ones--to
a deterministic behavior at small scales--the last cracks.
DOI: 10.1103/PhysRevE.71.046215 PACS number s : 89.75.Kd, 46.50. a, 47.54. r
I. INTRODUCTION
Macroscopic patterns often present an intriguing interplay
between a well-defined local organization and a globally dis-

  

Source: Adda-Bedia, Mokhtar - Laboratoire de Physique Statistique, Département de Physique, École Normale Supérieure
Laboratoire de Physique et Mécanique des Milieux Hétérogènes, École Supérieure de Physique et Chimie Industrielles

 

Collections: Geosciences; Physics