Critical Thickness Ratio for Buckled and Wrinkled Fruits and Vegetables

Fruits and vegetables are usually composed of exocarp and sarcocarp and they take a variety of shapes when they are ripe. Buckled and wrinkled fruits and vegetables are often observed. This work aims at establishing the geometrical constraint for buckled and wrinkled shapes based on a mechanical model. The mismatch of expansion rate between the exocarp and sarcocarp can produce a compressive stress on the exocarp. We model a fruit/vegetable with exocarp and sarcocarp as a hyperelastic layer-substrate structure subjected to uniaxial compression. The derived bifurcation condition contains both geometrical and material constants. However, a careful analysis on this condition leads to the finding of a critical thickness ratio which separates the buckling and wrinkling modes, and remarkably, which is independent of the material stiffnesses. More specifically, it is found that if the thickness ratio is smaller than this critical value a fruit/vegetable should be in a buckling mode (under a sufficient stress); if a fruit/vegetable in a wrinkled shape the thickness ratio is always larger than this critical value. To verify the theoretical prediction, we consider four types of buckled fruits/vegetables and four types of wrinkled fruits/vegetables with three samples in each type. The geometrical parameters for the 24 samples are measured and it is found that indeed all the data fall into the theoretically predicted buckling or wrinkling domains. Some practical applications based on this critical thickness ratio are briefly discussed.