Fractional derivative modeling for characterizing stress relaxation properties of Hami melon during drying

• Published in: Journal of texture studies 2023-12, Vol.54 (6), p.893-901
• Main Authors: Yang, Yumin, Yu, Jinghu, Zhou, Xingyu, Qian, Shanhua, Zhu, Fangyong
• Format: Article
• Language: English
• Subjects: Cucurbitaceae; Desiccation; discrete numerical solution; drying; Elasticity; fractional derivative model; Grünwald–Letnikov; stress relaxation modulus; Viscosity
• ISSN: 0022-4901; 1745-4603
• DOI: 10.1111/jtxs.12788

The viscoelastic properties of food materials will change significantly while drying is in progress, which greatly influences the food deformation caused by drying. This study aims to predict the viscoelastic mechanical behavior of Hami melon during drying using the fractional derivative model. To characterize the relaxation characteristics, based on the finite difference method, an improved Grünwald–Letnikov fractional stress relaxation model is proposed to derive an approximate discrete numerical solution of the relaxation modulus by applying the time fractional calculus. The Laplace transform method is used to verify the obtained results, and the equivalence of the two methods is proved. In addition, the stress relaxation tests prove that the fractional derivative model has a better prediction effect on the stress relaxation behavior of viscoelastic food than classical Zener model. The significant correlations between the fractional order and the stiffness coefficient and the moisture content is also studied. Which is negative correlation and positive correlation respectively. The fractional model is more accurate than the classical model in modeling the stress relaxation behavior of viscoelastic material Hami melon during drying, and the fractional order has an exponential relationship with moisture content and a three‐dimensional polynomial relationship with stiffness coefficient.