RESEARCH PAPER
A mathematical model of cocoa pod deformation based on Hertz theory
 
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Department of Agricultural Engineering, Obafemi Awolowo University, Ile-Ife, Nigeria
Publication date: 2021-08-19
 
Int. Agrophys. 1994, 8(3): 403–409
 
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ABSTRACT
A mathematical model based on Hertz's theory of contact stress was developed for the analysis of cocoa pod deformation when subjected to a uni-axial compressive stress, in its lateral axis, between rigid parallel plates. A two-sample t-test comparison of the experimentally measured values of the stiffness modulus and those obtained from the initial Hertz theory equations indicated a very significant difference, which was observed to be due to the irregular shape of the pod, its furrowed circumference and internal hollowness, contrary to some basic assumptions of the theory. Correcting factors developed to account for these irregularities significantly improved the predictions of the modified Hertz relation. The shape factor, which expressed the deviation of the material from a true ellipsoid in terms of the material contact area with the loading plate, was found to be the most critical correction factor in terms of which a combined correction factor could be expressed to simplify necessary computations.
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