Abstract
A sophisticated relationship between strain rate and stress in plant tissues subjected to mechanical loads reflects the structural complexity and properties of biological tissues. The aim of this study was to develop a mathematical model explaining the above relationship. A simplified, non-linear rheological model of a cellular solid characterised by elastic cell walls and the presence of incompressible fluid in cells was developed. In this model, changes in tissue deformation are determined by the elasticity of the cell wall, the ratio of cell wall thickness to cell diameter, the flow resistance coefficient and tissue porosity. Plant materials (discs cut out from fresh sugar beet roots, celery roots and potato tubers) were analysed to verify the model's adequacy. The developed model indicates that in samples with a constant volume during compression, stress in compressed tissue is determined not only by strain and strain rate, but also by the cellular structure and the shape of the sample. Further research is needed to test the model in other types of materials. The model should also be analysed for its sensitivity to cell size and shape, and the morphological structure of biological tissues.
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