Memory effect on the formation of drying cracks.

We propose a model for the formation of drying cracks in a viscoplastic material. In this model, we observe that when an external force is applied to a viscoplastic material before drying, the material memorizes the effect of the force as a plastic deformation. The formation of the drying cracks is influenced by this plastic deformation. This outcome clarifies the result of recent experiments which demonstrated that a drying fracture pattern on a powder-water mixture depends on the manner in which an external force is applied before drying. We analytically express the position of the first crack as a function of the strength of an external force applied before drying. From the expression, we predict that there exists a threshold on the strength of the force. When the force applied is smaller than the threshold, the first crack is formed at the center of the mixture; however, when the force applied exceeds the threshold, the position of the first crack deviates from the center. The extent of the deviation increases as a linear function of the difference between the strength of the force and the threshold.