Steffen Bohn

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.

Crack patterns, as they can be observed in the glaze of ceramics or in desiccated mud layers, are formed by successive fractures and divide the two-dimensional plane into distinct domains. On the basis of experimental observation, we develop a description of the geometrical structure of these hierarchical networks. In particular, we show that the essential feature of such a structure can be represented by a genealogical tree of successive domain divisions. This approach allows for a detailed discussion of the relationship between the formation process and the geometric result. We show that--with some restraints--it is possible to reconstruct the history of the system from the geometry of the final pattern.