A phenomenological model for the inelastic stress-strain response of a potato tuber

In this article, we synthesise concepts from the theories of plasticity, volumetric growth, and pseudo-hyperelasticity to develop a phenomenological constitutive model for potato tuber tissue. Here, particular focus is laid on the inhomogeneity of the constitutive behaviour across different anatomical zones of a potato tuber. The internal stresses are expressed in terms of an elastic contribution to the local strains and are controlled by a kinetic memory variable that traces the past strain history. Inelastic strains, by contrast, are considered as a combination of a plastic component and a pure volumetric component mimicking the eviction of fluid. Considering tubers of cultivar Belana, we identify the relevant constitutive parameters based on stress stretch curves obtained from single-cycle uniaxial compression experiments on samples extracted from different anatomical tuber parts. The stress strain response of the tissue is characterised by a pronounced and well reproducible hysteresis which displays slight stiffening along the initial loading branch. Considering the parenchyma microstructure, the significant reduction in tissue turgidity on unloading may be caused by the eviction of intracellular fluid from the parenchyma cells and an inelastic cell wall response. The experiments show that the inelastic volume change varies approximately linearly with the axial stretch. Additionally, histological analyses are presented in an attempt to quantify microstructural inhomogeneities. (C) 2020 Elsevier Ltd. All rights reserved.