Mean-field crack networks on desiccated films and their applications: Girl with a Pearl Earring
Usual requirements for bulk and fissure energies are considered in obtaining the interdependence among external stress, thickness and area of crack polygons in desiccated films. The average area of crack polygons increases with thickness as a power-law of 4/3. The sequential fragmentation process is characterized by a topological factor related to a scaling finite procedure. Non-sequential overly tensioned (prompt) fragmentation is briefly discussed. Vermeer's painting, Girl with a Pearl Earring, is considered explicitly by using computational image tools and simple experiments and applying the proposed theoretical analysis. In particular, concerning the source of lightened effects on the girl's face, the left/right thickness layer ratio (≈1.34) and the stress ratio (≈1.102) are evaluated. Other master paintings are briefly considered.