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A Relaxation Model Based on the Application of Fractional Calculus for Describing the Viscoelastic Behavior of Potato Tubers

Published by the American Society of Agricultural and Biological Engineers, St. Joseph, Michigan

Citation:  Transactions of the ASABE. 60(1): 259-264. (doi: 10.13031/trans.11951) @2017
Authors:   Wenbin Guo, Osvaldo H. Campanella
Keywords:   Fractional calculus, Potato tubers, Rheological model, Stress relaxation, Viscoelastic materials.

Abstract. Describing viscoelastic properties with rheological models is very important to understand the physical characteristics of fruits and vegetables for their storage, quality detection, transportation, and processing. However, in currently used models, a relatively large number of parameters is used to describe the viscoelastic properties of these materials, and finding the physical meanings associated with these parameters becomes difficult. In the present work, a simple model based on fractional calculus is proposed to describe the relaxation behavior of potato tubers. Data on potato tubers tested under relaxation tests are analyzed using this approach, and it is found that fractional calculus can be successfully applied to study the stress relaxation behavior of potato tubers. Compared with the generalized Maxwell model, the fractional model can describe the stress relaxation behavior of potato tubers accurately with only two parameters (α and k), which respectively represent the permanent deformation characteristics and elastic modulus. Statistical analysis indicates that parameters α and k are significantly correlated with the parameters obtained from the application of the generalized Maxwell model. Thus, the generalized Maxwell model can be replaced with the fractional model without losing accuracy, which is useful for the reduction of viscoelastic parameters in the data processing of stress relaxation tests.

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