Critical thickness ratio for buckled and wrinkled fruits and vegetables
Department of Mathematics, City University of Hong Kong - 83 Tat Chee Avenue, Hong Kong, PRC
Received: 7 July 2014
Accepted: 4 November 2014
This work aims at establishing the geometrical constraint for buckled and wrinkled shapes by modeling a fruit/vegetable with exocarp and sarcocarp as a hyperelastic layer-substrate structure subjected to uniaxial compression. A careful analysis on the derived bifurcation 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 buckled shape (under a sufficient stress); if a fruit/vegetable is 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.
PACS: 46.32.+x – Static buckling and instability / 81.40.Jj – Elasticity and anelasticity, stress-strain relations / 87.10.Ca – Analytical theories
© EPLA, 2014