Algorithms for generating planar networks simulating hierarchical patterns of cracks formed during film drying

Abstract

Hierarchical crack patterns that arise during the drying of thin films of colloidal dispersions or polymer solutions on a solid substrate are of interest both from a fundamental standpoint and in the context of the creation of transparent electrodes for optoelectronics. This paper analyzes the morphology of such patterns based on image processing of real-world samples. Graph theory is used to extract chains of edges and analyze the network topology. A method based on the hierarchy of connections is applied to classify cracks by generation. The limitations of existing classification approaches related to the discreteness of the time scale and the use of only a part of the entire pattern are discussed. Three approaches are used to generate artificial hierarchical networks: random uniform partitioning, recursive Voronoi partitioning, and a crack growth simulation model, each modified to reproduce the hierarchical structure. A comparison was made of the geometric characteristics (distribution of crack angles, edge lengths, cell areas, and circularity coefficient) and topological properties (distribution of the number of cell sides) of real and simulated networks. It was shown that the simulation model best reproduces the key features of real cracks, including the characteristic right angles of their connections.

Figures (11)

• Figure 1: a) When a thin film of a colloid or a polymer desiccates on a horizontal solid substrate, a gradient of solvent concentration occurs inside this film due to evaporation of solvent from the free surface of the film along with diffusion of solvent from the bottom of the film to its top. Solvent loss leads to a shrinkage of the film and emergence of mechanical stress inside the film. b) Example of a crack pattern (craquelure) in painting. c) When soil desiccates, a gradient of moisture concentration occurs inside soil due to evaporation of water from the free surface of the soil along with diffusion of moisture from the depth to the surface. Moisture loss leads to a shrinkage of the soil and emergence of mechanical stress inside the soil. d) Example of desiccation crack pattern in soil.
• Figure 2: Clear hierarchical crack pattern on a painted wall.
• Figure 3: Examples of situations where the classification Bohn2005 has to fail: a)--c) stars, d)--f) loops.
• Figure 4: Cracked ceramic glaze on the internal surface of the plant pot. The hierarchical nature of the crack pattern is clearly visible.
• Figure 5: Examples of hierarchical networks obtained from images of real-world crack patterns a) based on Yang2025; the sizes of each original image are about $4.4 \times 3.3$ mm; b)based on Yang2025a; the sizes of each original image are about $8.9 \times 6.7$ mm. In all cases, classification of crack generations was performed using the algorithm Bohn2005.