Constructal theory of natural crack pattern formation for fastest cooling

The constructal theory of the origin of geometrical form in natural flow systems is used to predict the formation of crack patterns in solids subjected to volumetric cooling by convection. The approach is purely theoretical (deterministic), because it starts from the principle of geometric minimization of resistance to flow, and leads to the existence of optimal distances between successive cracks and, consequently, optimal crack widths. The analytical part of the paper is based on the method of intersecting the asymptotes (many cracks vs. few cracks), and anticipates several natural features that had not been explained previously: cracks are denser when the convective cooling effect is more intense and/or the initial departure from equilibrium is greater, and the loops are close to round (or square) in two-dimensional lattices of cracks. These trends are further illustrated by using a one-dimensional numerical conduction model with equidistant parallel-plate cooling channels. (C) 1998 Elsevier Science Ltd. All rights reserved.