Coupling analysis of pattern formation in desiccation cracks

Desiccation cracks are widely observed as a result of the drying process of the mixture of powder and water. These cracks have a net-like structure and tessellate the dry-out surface area into polygonal cells with typical size. Regardless of the choice of the materials and the minor details in the drying process, while some varieties can be observed, the basic topology of the cells (i.e., net-like structure and the polygonal cells) is persistently conserved. This stable and common feature in the desiccation crack patterns strongly suggests the existence of the common governing mechanism behind. In this paper, the pattern formation of desiccation cracks is regarded as the result of the coupling among (i) the change in water volume fraction due to desiccation, (ii) the equilibrium of deformation field corresponding to the inhomogeneous volume shrinkage, and (iii) the crack formation. Based on this assumption, a coupling model of desiccation, deformation, and fracture is proposed for the numerical analysis of the desiccation crack patterns. We perform the coupled analysis by using finite element method for the desiccation (described by the diffusion equation) and particle discretization scheme finite element method (PDS-FEM) for the seamless analysis of deformation and fracture. The results of the numerical analysis show satisfactory agreement with the experimental observation in terms of the basic topology of the cells and the hierarchical sequence of the crack propagation. These results indicate that the proposed approach captures the fundamental governing mechanism of the pattern formation of the desiccation crack phenomenon.